there's been some good replies to this thread but I'm going to add my two cents. I was a grad student at SU for four years. I lived off campus every year, though each time in generally the same neighborhood. i would highly recommend living near Westcott. it's a small neighborhood about a mile east of SU. it's small but it's got two great cafes, a good bike shop, a venue for regional/local acts, and a couple solid places to eat. some houses are in rough shape so i'd definitely check em out before you sign on. i'd also recommend living by barry park. there's no bars or restaurants but its quieter, got more grad students, and you're likely to find a nicer place to live (if you care about that sort of thing). housing near the university, especially on euclid, can be rugged. it's also pretty loud. the undergrads at SU are animals. i never did myself, but i had a couple friends that lived downtown in very cool apartments. i don't think they were that expensive. you had the option of taking the bus or driving. i always thought the buses in syracuse were fantastic. they run in snowstorms and don't stop service until pretty late at night. they're also free to SU students. downtown's got a pretty solid bar scene for a small city. it's also got a couple good restaurants but for some reason they can get pretty pricey.
if you're a cyclist, syracuse has incredible riding. i've lived in north carolina, massachusetts, and new jersey, and outside syracuse is some of the best terrain there is. the roads are in fantastic condition, it's scenic, and there's almost no traffic. of course the main difficulty with being outdoorsy and liking warm weather sports is that the syracuse winter is BRUTAL. the first winter i was there we had a total of 15 feet of snow for the season. one time it snowed for 4 days STRAIGHT. you could go a couple weeks without seeing the sun. the good thing is syracuse has got some big time athletics and going to games at the carrier dome is a ton of fun.
syracuse also has a ton of awesome diners (mother's cupboard, the egg plant, stella's, etc.), a top notch farmer's market, destiny usa (a crazy big mall, which is actually kind of cool), and the everson art museum. the cost of living is low. the most I ever paid for rent was $500 to share an apartment with one other roommate. most places will charge you $4-5 for a pint of beer. there's plenty of good, cheap food shopping (wegman's, asian grocer's, price chopper). you don't NEED a car but it's certainly nice to have one. if you do have one, four wheel/all wheel drive is highly recommended.