"NY Botanical Garden and Arthur Avenue in the Bronx"

A better option, I think, would be the Brooklyn Botanical Garden which is easy to access by subway and has an entrance next to the Brooklyn Art Museum, also very much worth a visit.

On your way back to the city, check out Brooklyn Heights and Dumbo from where you can access the foot path on the Brooklyn Bridge.

HTTY

A visit to Queens can be very worthwhile. Flushing - the last stop on the #7 train is like stepping into a great Asian city with some of the best Asian eating in the world and all sorts of interesting shops. Also Roosevelt Ave/Broadway area - very multi-ethnic and again - all sorts of great ethnic eating. BTW - this is becoming the real New York City with a new immigrant population bringing their food, culture, et al with them.

Ride the Staten Island Ferry
Forbes Gallery
Free Kayaks at Pier 40