Well if you search for Arusha, you would see this very recent thread discussing how to get there from Nairobi.
http://www.flyertalk.com/forum/afric...bi-arusha.html
It's a very easy drive. You can get a driver to take you, or take a bus or rent your own car if you will be coming back to Nairobi. As for airfare to Nairobi from NYC, it's only about $800 each on TK which is a good airline in the Star Alliance. Or $1300 on Virgin.
You could get a cheap one-way flight from Zanzibar back to Nairobi and perhaps enjoy a couple days there in a nice hotel before you fly back.