I don't think a mt bike is necessary for the vineyard. About 14 years ago myself and my then boyfriend parked the car in Woods Hole, rode our bikes to the ferry and ferried over to Oak Bluffs (but stayed in Edgartown) and rode all over the island. We had the best time ever! We had mountain bikes with big knobby tires because that is all we owned at the time. The knobby tires provided much more resistance vs. the surface we were riding on but we knew this, dealt with it, and just had fun. All we had with us was what we could take on 2 panniers per bike. However, we rode entirely on the main paved roads and never encountered rough stuff but nor were we looking to do any off-roading. Hills there are not bad. We did not do bike paths and I can't recall how many actually existed that many years ago. We did jump a boat over to Nantucket for a day and there was one area where we were glad we had the mt. bikes instead of road bikes.

If you are looking to zoom around the island with not much gear, or have a road bike that can accomodate a small pack, take a road bike. If you are looking to take your time a little more without a need for speed to destination, and want room for "shopping items", take a commuter with slick tires. You will still be able to explore quite nicely from town to town that way as well.

Martha's Vineyard is beautiful and you will have a great time no matter your choice, as long as you go with the flow with whatever choice of bike you choose to take.