Nantukett is primarily a relaxing place, so it has great beaches and restaurants.

Restaurants, Dining
All of these recommendations are in Town (Town is the main downtown area on Nantucket).

Breakfast
Downey Flake
Skonset Cafe

Lunch
Black Eyed Susans (call for reservations)
Skonset Cafe

Dinner
21 Federal (call for reservations)
Boarding House (dinner and nightlife)

Nantucket Inquirer and Mirror (local newspaper) Restaurant Guide:
http://www.ack.net/restaurant_guide.html

Maps of Nantucket
Yahoo has a great map of Nantuckett and Google has a great satelite view map of Nantucket as well.

Nantucket Beaches:

Nantucket is famous for its drivable beaches. You'll need a permit (get one at the police station in Town) and you'll need to deflate your tires first. Great Point, Smith Point and Eel Point all are drivable beaches.

Surfside and Jetties are good family beaches and both have snack bars. Jetties is the best for small children - very low waves exist because of the location.

Sisco is known as the surfer's beach and has a young adult crowd.

Other things to do:

Athletic types may want to try the Nantucket Surf School (508.560.1020).

When you get sick of the beach, try the famous Nantucket Haunted Hike a walking tour given by "amateur parapsychologist" William Alexander.

Maps of Nantucket
Yahoo has a great map of Nantuckett and Google has a great satelite view map of Nantucket as well.

More things to do on Nantucket:
Islandofnantucket.info