This is a real concern for many of us — moving to a new place and job can be so lonely in any case, even without the pressures of academia. There are two thoughts that come to mind.
One, there is value in friendships both within and without the academy. I found that making friends at church, through small group study, was very helpful. It was years before I made good friends on my own campus. And now that is also very good — to have dear friends who I work with and can see for lunch on a regular basis.
The second thought is that friendships take time. There can be a "shoulder season" between easing into a new stage with your grad school friendships and making mature friendships in the new location. That's a bit painful and hard. When I moved to my current job after grad school, I remember saying, "I don't need any new friends! I have made all the lovely friends I want." Of course, I had to transition from those close grad school friends to some people who could be part of my joy and fun and support locally.
Looking out intentionally for people to be friends with is part of it. I highly recommend noticing people (not just other teacher or professors, but people in career services, administration, other departments, etc.) who you think would be fun to interact with. Ask if you can go to lunch with them or coffee or whatever to pick their brain about the school, etc. Those conversations can be "safe" and can let you know if they are someone you'd like to do more with.
Making some of your other life commitments count for friendship can help too. Use your church, exercise, or hobby time to overlap with friendships. Is there someone around who likes biking or walking who you could suggest a meet-up with for one of those activities? I joined a book club with non-academic professionals in my city within a couple years of moving here. My veterinarian had invited me. Those women are a great source of friendship, even though I don't see most of them outside our monthly meetings.
I think more people are looking for friendship than we can imagine. Showing up in the same place regularly — community service opportunities, church, gym, etc. — can provide us with an idea of who we might have some rewarding conversations or time with. I can't emphasize enough that just being on the lookout for someone to be friends with can reap huge rewards — they may feel the same way. My best friend in my current institution was a new hire in a different department who saw me in the hallway, complimented my outfit, and then said, "I've seen you around and I think we need to be friends." I followed up with an email invite to lunch and we've been best pals ever since, even though her pre-schoolers and my crazy schedule mean we don't see each other as often as we'd like.
Friendships are vital. I have a Christian friend who's given this a great deal of thought. I recommend her website girlfriendcircles and her book, Friendships Don’t Just Happen: The Guide to Creating a Meaningful Circle of GirlFriends.
Yes, you're busy. But you've correctly identified that finding someone to walk life's path with (or several someones, but just one good friend goes a long way!) It is part of what makes it possible to live an abundant life.
One way to handle this is to mix work and pleasure. For instance, you could initiate (or get in on) a faculty group that reads and critiques one another's writing, or reads and discusses important scholarly work in your area. The issue there is that you may not want to be friends with the particular people that would involve.
I actually prefer this second suggestion, since intellectuals really need to surround themselves with a wider variety of types of people, in my opinion. Get involved with service at your church, and make friends through that. We all need to be doing that anyway, even if we're in a season where we're protective of our time. I'm a busy working mom myself, so I just get the kids up at 5:30 a.m. on Sundays and we go serve breakfast down at the shelter with other volunteers from church. It doesn't really take more time, since we wouldn't normally get up that early anyway. We go straight to the 8 a.m. service, and we're done with church by 9:30 (plus we get to eat there!). Other ways of serving that wouldn't involve an extra evening might be to do something at the service itself, like greeting, reading, or serving on the altar guild. (Can you tell I'm Anglican?)
Of course, you still have the issue of how you're going to spend time with these new friends once you have them. Try doing things you need to do anyway, but do them together. You've got to eat, you've got to study, you've got to take breaks now and then. Does someone you meet also need time for studying? Make it a date at Starbucks (if you can both be silent for long periods of time). It might actually work as accountability as well. Do you know you've got a writing day and that your brain might turn to mush? Schedule a coffee at the time you'd usually be having some sort of nervous breakdown. Chat with a new friend and then come back to your work refreshed. I've even asked people to come talk to me while I do housework. Heck, they might even help you fold your laundry.
I've done better with keeping in touch with old friends than making new, and my response here brings additional questions. For me, as is likely the case for most people, I had more time for making friends during graduate school, but it has little to do with the hours I spend doing research.
Since grad school, I married and had two kids. Both of these events drastically changed the friend landscape for me as we moved away from UW-Madison. How do two people let alone four people make friends? I remember as a child my family had whole families as friends. My parents usually knew two or three families with children in the same age ranges, and we all enjoyed spending time with each other. I thought this was normal, but as an adult, I'm figuring out how special those relationships were.
Individually my husband or I could make friends, but why is one member of a couple inevitably a challenge? And then, mix in the children. When the kids are old enough for friendships, if the problem isn't serious behavior issues, then the age differences of the kids are just too big or they have no interests in common at all. So we don't often visit as a family with other families. And if we do, we usually have to schedule about a month in advance to coordinate the eight (or more!) people's schedules.
For making friends, because we don't live very close to work or church, most of my communication is by e-mail or phone. This is very different from grad school where I could often grab lunch or dinner with a friend on campus. Quality time is one of my love languages, so I miss not having face time with my friends. But I’ve found even quick notes or phone calls go a long way toward establishing meaningful relationships.
Because I’ve been in places were I was unable to find close friends that understood the pressures of the academic life, I have found that keeping in touch with old friends was something that I needed to do. Because I am very bad at keeping in touch with anyone — even family members — unless I have a regular schedule, I formed an online prayer and accountability group with a few of my grad school friends. On the first Sunday of the month, we Skype and give updates tracing God's hand through the events of the month. Then we pray for each other as we had done when we met face-to-face years earlier. We try to follow up with each other between Skype sessions with e-mails, phone calls, and even snail mail, but we always know we can count on our Skype call for touching base again.
As someone who is starting a second year on faculty in a new city, I can relate to your dilemma. I, too, find myself struggling with finding time for friendships (and life in general) amid the writing commitments, class prep, and the like. Frankly, there are weeks when finding time to go grocery shopping feels like a small victory.
That is probably why I was a little reticent about meeting a woman at my church for coffee one afternoon — I just wasn’t sure I had the time. But we shared similar interests. In fact, although she works at a different university than me, we actually work with writers in the same historical period and location. So I carved out an afternoon and went to say hello. I’m glad I did. Over the course of my first year here, she’s become a great friend. She’s counseled me through some tough life changes, helped me paint my living room when I bought a new house, and we’ve even tried our hand at woodworking when we built an end table one evening (it turned out great!).
I don’t think there are any easy tricks or shortcuts to friendship. A good friendship grows slowly, and only with much love, patience, and attention. It’s always worth it, though, because there is no substitute for a good friend. As I was thinking through your question, I took a brief foray through my Bible’s concordance entry on friendship, and was reminded that valuable friendships are deep and close, and a good friend offers correction, guidance, and support through the tough times (Prov 18:24; Prov. 17:17, Eccl. 4:10). In other words, friends help us live.
Even though I know all of this, and even though I’ve struck up friendships with a few people in my new city over the course of my first year here, I confess that I’ve never quite managed to hush that tiny, exhausted-sounding voice that tries to convince me that I don’t really have time. But I am beginning to suspect that I need to radically rethink how I approach time in my life.
I tend to think of time as a fixed quantity, of which there is never enough. But the more I think about it, the more certain I become that my time, like everything else in my life, will multiply as I surrender it to God and use it to follow the things that seem to be important to him — like friendship. After all, God has provided all sorts of things for me over the years: why not time? I’m guessing that I already have all of the time I need to accomplish the tasks God has for me, even when it doesn’t feel like it. I think I’m going to try trusting in that a little more this year.