Try DeWitt, as it is a suburb this close by and there are some apartments on Nottingham Road. Out of the suburbs you picked, I think Liverpool is the better in terms of getting to campus and back. It's a bigger suburban area than Camillus too. Liverpool is in the Northern suburbs, Camillus is in the Western suburbs and DeWitt is a Eastern suburb. If you do live in the city, try the Westcott area. Also, apartment complexes like Clarendon Heights, Greenwich Manor and Nob Hill aren't bad and are close to campus.
Here is a website to check out:
http://www.bestapartmentsinsyracuse.com/
It has apartments in Syracuse, Liverpool and a few other suburbs.