There are a few hotels on or near campus - 1) the Sheraton is on campus, walking distance to the carrier dome (which is right next to the law school) and 2) The Gennesse Grand, which is very close to campus, and 3) the Marx, which is right by the Gennesse Grand. You can really walk to campus from the Gennesse Grand and the Marx but it would be a steep uphill walk. I'm not sure about pricing, but all of those tend to be on the nicer side for the area. I also don't know about pools - sorry. There are a lot of restaurants downtown and also by the university and there is a kid's science museum downtown, too.
Like PP said, the Carousel Mall is in Liverpool which is a 10-15 minute drive on I-83 from SU. If you are near the mall, there is a fantastic diner for breakfast - Stella's - really inexpensive and long lines (call ahead to get your name on the list). From what I remember, there are a bunch of chain hotels in liverpool and I would just look online for reviews. I do not recall any hotels right near the mall but since I lived there I wouldn't have noticed.