First, it's a base, not a campus. This is the military. Once you get through boot camp, you can leave after class is complete, which marks the end of your workday. Keep in mind you will also have homework to complete, which must be done in the classroom, and depending on your academic performance you may have mandatory study time, so typically weekends are your best bet for leaving the base and doing stuff.
You will not be able to bring anything with you to boot camp. Once you're in A School, you can have things shipped to you, or go out and buy them, but there's limited storage space, so you might not have more than the bare necessities. You absolutely will not be allowed to bring a musical instrument into the classroom area of the school, but there are places on base to play, but you will probably annoy everyone and wasting study time.
FYI, there really isn't much math and science once you finish power school, so if you're really interested in that, you might want to find a different job. Nukes are operators and maintenance technicians.
