What school will you be attending?
As many have said, "Get thee to the University Outing Club!"
Like you, the other members will be poor, need to schedule around classes, finals, Spring Break, Winter Break and summer vacation.
As such, they will do lots of ambitious, weekend trips by carpooling to different near- and medium-distance locations during the school year and will plan some longer-distance, longer-duration trips for Spring and Winter Breaks.
Compared to other non-profit, volunteer-led groups that organize trips like the Sierra Club, University Outing Club members tend to be much younger, healthier, poorer, hornier, and fewer of them have cars. So you gravitate towards the same kinds of trips and destinations.
I hung with the UC Berkeley Hiking Club for many years during my various stints there. Professional, 9-to-5 friends would be amazed at the kind of trips we'd do almost every weekend when all they'd managed to do between beer:30 on Friday and 8 am Monday was to mow the lawn and rent a movie.
Our outing club had gear to loan out (for free), you quickly make friends, and they will loan you gear, even clothing. This obviously saves you money initially, but it also is a huge savings to buy the RIGHT gear for your adventures, body, and metabolism the FIRST time aided by having tried many of the options out there.
Do some day hikes with the group. Then do some overnights. There are people you WANT on your trip (they offer to drive or pay for gas; they do more than their share of cooking and cleaning, they host events at their house, they are cheerful and enjoy getting to know other people). Be that person. Then, a month or two in, if the trips aren't as mountaineering-ish as you want, you can suggest some easy peak-bagging, followed by more ambitious trips. Often, it just takes someone with desire and a willingness to suggest a trip, EVEN THOUGH THEY AREN'T EXPERT AT THAT KIND OF TRIP (yet). We had two members who really wanted to learn to cave and 6 of us really got into it, learning on our own, doing easy stuff first, seeking out resources, and doing more and more challenging trips.
My wife and I are one of at least 4 couples who connected through that club and who are still together 20 years later.
If in a large city and your university doesn't have an active club, find out about the other colleges in the area. All such groups I've known welcome any like-minded hikers/backpackers/climbers regardless of student status or affiliation.