I would not recommend 3 days unless you are chartering a fishing boat or something. Spend one night at the most if you are just visiting.
Its small and a little weird. "Dry" Island but you'll see the locals rolling around with half hidden cases of beer in their golf carts.
Crisfield is nearby and a has a fun little downtown and some charter boats. Late summer is a good time to fish, lots of action near the harbor.
This is a great place to see the effects of rising ocean levels... shrinking real estate
Tangier is a tiny, flat, low lying island that is very susceptible to hurricanes, flooding and erosion. Those islands naturally come and go, I have been boating and fishing in that area since I was 10 years old. It used to be somewhat wealthy but the availability of cheap seafood from foreign countries and pollution in the bay has really put a hurtin on their economy.
I drop by once every few years. Its fun to walk around and grab a bite to eat.