All the info on cross training is great; core, antagonist muscles, lockoff, etc. However, cross training and less-climbing-specific exercises like that are SUPPLEMENTS to training in a bouldering gym, not substitutes. For me, living as a poor grad student in a large city that was several hours away from real rock, a good gym was essential to breaking into and staying at a 5.12 level.
All the exercises listed in this thread are great you'll be on your way to one armed lockoff front levers in no time, and if you add hangboarding into it, your fingers will be super strong, too. But here's an interconnected list of what you'll be lacking:
-Power/contact strength: the ability to explode from one hold to the other, and to latch onto a small hold quickly.
-endurance: yes, if you do the right combination and duration of repeaters on a hangboard, you'll have the endurance to hold onto small holds for a longer time. But you will be lacking power endurance, the ability to move smoothly and quickly through sections with enough reserves to fire that crux.
-technique: this is particularly important if your goals include trad, or more heady routes. You'll need to be dialed into footwork and body positioning that keep you moving as efficiently as possible through possible finicky gear placements and runouts.
-headspace/psychology: like technique, this is hard to quantify, and if I may extrapolate, the fact that you're college age, and have probably been climbing for less than ten years, makes it all the more critical to keep working on the mental aspect of climbing.
None of these things can be efficiently trained with a home setup, or cross training. You COULD build a campus board, which would be my first advice, and it would definitely work our power. If you have the money and space for a campus board, by all means do it.
But overall, I would say if you want to stick to 5.12 trad, and possibly improve, just suck it up, take out a few more student loans, and stick with a gym membership. Climbing consistent 5.12 is worth a couple thousand dollars at the end of your college career.