Martha’s Vineyard has two low-cost alternatives for accommodations – a campground and a hostel.
The Martha’s Vineyard Family Campground is in the town of Tisbury, with a bike path and bus stop out front. The campground offers campsites, parking sites for RVs, and cabins. It’s open from May thru October. Reservations are suggested. http://www.campmvfc.com/
The Martha’s Vineyard Hostel in West Tisbury is right off the bike path, with a bus stop out front. Rates are as low as about $25 per night. The hostel is open from late April to mid October.