A good day out can be found on Governor's Island. You can get there for free on early weekend ferries from Brooklyn and Manhattan, $2 round trip after or $6 each way on East River Ferry. The island is federal park land and you can spend hours just walking or riding bike round the island. There is lots of public art and many of the buildings house art galleries. Often you can find artists at work along the way. There are food trucks with lots of good, reasonably priced food, a really cool beach bar where they sell snacks. It comes complete with palm trees, volley ball nets and kooz ball. There are benches and tables and all weather couches. You can even bring your own food and eat here or picnic anywhere. If you are a history buff there are several tours, also free, of forts and island.
After a day in the sun, there are plenty of good reasonable dinner places in Brooklyn, lower Manhattan or anywhere ferry stops. All you need is a metro card and some energy.