New Haven has a great food scene and the best pizza in the world. There are several museums, theaters, and concert venues around the Yale Campus. I would recommend checking out Toads Plcae

You can also get an Uber to Hammonasset Beach State Park which has a great nature preserve. There might also be a bus line that stops there.

From new haven you can also visit several local breweries like NebCo and Two Roads. You can also catch a metro north train the NYC, but you could easily.