Oneonta is a small city ... about 20,000 people live there. It's built on the hillside with the two colleges (SUNY and Hartwick) up near the top of the hillside. The colleges are close to each other. The shopping areas (grocery stores,
Walmart, etc.) are on the outskirts of town, and not really within walking distance of the campuses. There used to be a LOT of bars in the downtown area (which is easily accessible from the campuses) but many of them have closed in recent years due to crackdowns on under-age drinking.
Soccer is big there (the National Soccer Hall of Fame is there), with large playing fields in Neawah Park down near the river (Susquehana).
It is very rural outside of the city limits, although there is some sprawl on "South Side". It is about an hour's drive to Binghamton to the southwest, and slightly more to Albany to the northeast (both accessible via I-88). SUNY Cobleskill is about a 1/2 hour away (on the way to Albany). Cooperstown is about a 1/2 away as well.
Oneonta can be a dreary sort of town ... downtown has deteriorated quite a bit over the past 25 yrs, and there isn't a whole lot down there any more. Personally I wouldn't recommend SUNY Oneonta unless there was a program there that your child couldn't access elsewhere.