Mikey, I think you would enjoy Cancun. You can go out and party and your parents can relax in the hotel. I would recommend you stay somewhere in the hotel zone - where all the big 4/5 star hotels are - rather than outside, since that is where all the action is. Legal drinking age is 18 and they don't seem to be very strict so I am sure you will get in most places. Try one of the Fat Tuesday parties...

June/July will be very hot, upside is that it will not be crowded, and you may find you have some places almost to yourselves.