From mostly flat terrain down-Island (eastern end), to hills up-Island (western end), you will find the Vineyard a beautiful place to explore with a bike.
The dark lines on this map indicate the main bike paths. You can of course bike the other parts of the Island but those roads are shared with cars. From short rides flat rides like the 3 miles from Edgartown to South Beach (Katama), or long hilly rides like the 20 miles across MV from Oak Bluffs to Aquinnah… you can find a terrain and mileage that meets your criteria. Martha’s Vineyard is 100 sq miles, it cannot be biked in a day.. at least not to my knowledge.
One of the prettiest bike paths is the 6 mile stretch from Oak Bluffs to Edgartown… for a good part of the ride the ocean is on one side and Sengekontacket Pond on the other… it’s just lovely. Another pretty ride is the 8.5 mile ride from Edgartown to W Tisbury which goes alongside the state forest
You can rent bikes at several locations in Oak Bluffs, Edgartown and Vineyard Haven.
So get a bike, grab a map and let biking on the Vineyard put a smile on your face.