I thought it was harder to get into Binghamton than to get into Stony Brook University 
What are the chances of making it off Stony’s wait list?
I would much rather go to Stony Brook if accepted, and it’s my top choice university right now. Also when do students start to hear back from Stony Brook regarding the wait list decisions?
College admissions are fickle and unpredictable. You cannot reasonably expect to hear from SB until after May 1. If that is your top choice you can email a letter of continuing interest to your admissions representative. Let him/her know that you remain interested in Stony Brook, if you have any notable achievements since your application was filed you can mention them, you can note something you particularly like about the school or something you feel you can add to the school, and if true say “if accepted I will attend”.
In the meantime I’d send a deposit into Binghamton if that is the top choice of the schools you have been accepted to. I would assume you will attend the school you deposit to. Fortunately with an acceptance to Binghamton, you have a great back-up plan to Stony Brook so whatever happens you should be in great shape.