I did my undergrad there, so I'm not entirely sure what is best for vet students, but I can give you some info about it.
In terms of OCH, there are a couple grad student dorms (like the townhouses firefly mentioned, hasbrouck apartments etc). They're mostly located on north campus, and some of those cater to families as well. I don't know too much about them, but in general most of Cornells OCH is decent, though it can get expensive depending on what you choose. Its my personal preference to live off campus though, which I think most people do in vet school. There are tons of off campus apartment options all around campus, so you'll be able to find something that suits you. Most undergrads live in Collegetown which is south of campus, so unless you want to live in that sort of environment, I'd advise against living there. Rent gets stupidly high unless you live on the fringes of collegetown, and it can get rather rowdy on the weekends. It's also not super convenient locationwise, as the vet school is on the east side of central campus, which took me about 30 minutes to walk from the heart of collegetown. I knew a few vet students that lived east of the vet school off of dryden road (there's an apartment complex near there that I used to walk dogs in) that are super close to the vet school and in a much quieter area. Some of my other vet friends also lived in off campus apartments and houses closer to north campus.