Air Nav is the place to check. It lists the flight schools, FBO's etc. The best part is the comments sections that mentions places to eat etc
Most places want a check out, 45 minutes to 1.5 hours. Contacting them ahead will make it go faster. Bring your log book. Currently a late model 172 SP is around $115 wet.
Block Island is always a nice day trip, as is Montauk. The Hudson River corridor is great. Get the New York Terminal chart it gives the details.
Ocean City New Jersey, park and walk to the beach. (Also Ocen City MD)
A great spot is Blairstown NJ. Good cafe, gliders and a very pleasant rail trail running along side the strip.
Andover is nice to tune up your technique, 2000 ft with a lake at each end.
Cape May New Jersey is kind of quaint if you do quaint. Some very good restaurants.
Have fun
20driver