You can see much of MV on bikes. (Any of the shops near the ferry are fine.) However, I don't believe a single visit to MV would be complete without a stop at the Gay Head lighthouse (at sunset, if practical). That's a 40-mile round trip from the ferry, includes some hefty hills and a few narrow roads and doesn't take into account the extra miles for visiting Edgartown. Thus, if you’re planning to do this as a day trip, I would recommend a car, unless an additional $100 or so (net of what bike rentals would cost) would break your budget.
If you are going mid-week, consider taking your own car. You can make reservations
here. It will cost $130 to $150 for the car, but might be more convenient than renting a car on MV and, believe it or not, just as inexpensive! (Check out "Martha's Vineyard" rentals (choose Oak Bluffs) at, for example,
www.Budget.com.)
Forget about taking your own car on the weekend. Although a few non-reservation cars get on after long waits in line, summer weekend space on the ferries is booked months in advance.
While on MV, be sure to wander the downtown streets of Edgartown, stroll past the "gingerbread" houses in Oak Bluffs and enjoy the many coastal vistas around the island.