The island is small, so don't worry about which town you book in. Cabs and shuttles are plentiful and can be easily arranged. There are also very good (and cute!) public buses available around the island
A few of the many nice hotels on Martha's Vineyard:
Harbor View Hotel, Edgartown
http://www.harbor-view.com
Mansion house, vineyard haven
http://www.mvmansionhouse.com
lambert's cove inn
http://lambertscoveinn.com
beach plum inn, chilmark
http://www.beachpluminn.com
Menemsha Inn, Chilmark
http://www.menemshainn.com
Captain Flanders House, Chilmark
http://captainflandersinn.com
There are many other bed and breakfasts, inns, and hotels on island. A simple google search will yield many results.
vacation house rentals
For a more personal and economic stay on the island, please check out VRBO for vacation home rentals - this is especially good for groups of guests attending together!
http://www.vrbo.com/vacation-rentals/usa/massachusetts/martha-s-vineyard
Hotels tend to book up on the island during the summer, so please BOOK EARLY if you plan on joining us!