In the basement. It's about the only place it'd actually fit anyway plus where it is right now isn't optimal to begin with (in a high traffic area where it also shakes every time someone walks by). I'm not moving out anytime soon so that's something to worry about at a later date.YESSSS!!! another person doing a 125gal project!!! Mine is going very slowly, but will be interested in watching your progress!!
Where are you planning on setting up the tank? Another option, if you're still living at your parents' place, is to try and make it as low-effort for them as possible and they may be ok with you leaving this particular tank there, at least until you are done with the "apartment living" phase of your life (which I realize for some of us lasts longer than for others).
Not jumping on anything just yet at any rate, waiting until a good deal comes across on Craigslist, see large tanks floating around on there all the time.