If you don't bring your car across on the ferry, you'll need to figure out some island transportation. The ferry runs alternately to Vineyard Haven and Oak Bluffs, so if you're staying in either of those towns, you could probably walk or take a taxi to your hotel. Places to eat are also readily available in those towns.
If you are staying at a more out of the way place "up island," you might want to think about renting a car. Hertz is available at the airport, but Budget (www.Budgetmv.com) has locations in Oak Bluffs and Vineyard Haven as well. All the other rental car companies are local, non-national businesses. A list is available at www.mvy.com/islandinfo/getaroundtaxis.php. When I looked around, I found Budget to be the cheapest, as most of the local places specialize in scooters and jeeps and other fancy rides.
Buses are another way to get around the Vineyard, if you have some patience. You can get most places, but it might take a while. Bus info can be found at www.vineyardtransit.com.
Biking is yet another option, as the island is pretty flat and not that large. Bikes can be brought on the ferry or rented on the Vineyard. The buses all have bike racks as well. A word of warning though, roads are windy and shoulders are narrow to non-existent, so its not for everyone (I think it looks bloody terrifying!).
If you end up planning your trip so that the only reason to rent a car would be actually getting to and from the wedding (it'll be "up island," near Chilmark), let us know. We will be setting up some sort of shuttle to take care of that.
