You are going to love Nantucket! My daughter and I took our boat up and spent July there last summer.
Nantucket harbor is quite large and quite busy with multiple ferries, fishing boats, visiting cruisers under sail and power ranging in size to over 160 feet, a large fleet of small sail boats and lots of dingies from boats at anchor or in the extensive mooring field. The harbor is not as protected as one might assume. A visiting boat has three choices: anchor in the designated areas in the harbor, rent a mooring from Nantucket Moorings or rent a slip from the Nantucket Boat Basin. I have never anchored out so I can't speak to that option. But I have used both of the other choices extensively and here's my observations:
Nantucket Moorings -
http://www.nantucketmoorings.com/
Use the website to make a reservation as early as you can if you intend on visiting over a weekend. During the week, excepting possibly the week of July 4, you should be able to get a mooring with little or no notice. Not because it's not popular but it is a big mooring field.
When you pass Brandt's Point coming into the harbor hail Nantucket Moorings on Ch. 68. They will direct you to "green can 9" where one of their boats will meet you and invite you to follow them to your mooring. Keep in mind that they are "off the water" at 5 p.m. and it is much easier, particularly the first time, to find your mooring with them guiding you! (Voice of experience talking.) The moorings have two heavy lines streaming off a good size ball. You'll need someone on the bow with a boathook and some reasonable strength to heave up the mooring line but they seem to be replacing the incredibly heavy old hemp with nylon that is much lighter and no less strong.
With your mooring secured you can choose whether to deploy a dingy or call the Harbor Launch, also on Ch. 68. I have to tell you that I love the Harbor Launch. They always arrive within about 10 minutes, are piloted by very nice people and deliver you to their very convenient dock minutes from everything. For this you have to pay of course. My recollection, which may be wrong, was that individual trips (one way) were $4 and 8 one way tickets cost $30 last summer. There are bins at the launch dock for recycling and trash. The Allserve Boat (Ch 69) will deliver ice, water, groceries, coffee - pretty much anything to your boat for a fee. And, of course, there is a pump-out boat on call (Ch 9/14). Pump-out is free, tips are appreciated.
Nantucket Boat Basin -
http://www.nantucketboatbasin.com/
Unquestionably one of the finest facilities of its kind on the planet, the only beef I've ever heard is the price. That said, it is full or darn close to it from mid-June until Labor Day. And, it's the only game in town.
After you get your reservation, print out a map of the docks found on the website. The morning of your arrival call them and ask them to give you your slip number. As with the mooring field, when you pass Brandt's Point hail them and advise them of your arrival on Ch 11. They will advise you if there is any delay because of departing vessels and will arrange for the "dockettes" to meet you at your slip to handle lines, power cords, water and cable hook-ups, deal with paperwork and answer questions. "Dockettes" by the way is the name bestowed by George, the Harbormaster, on the very nice and very professional girls who work on the docks.
From the boat basin you are in walking distance of everything the town of Nantucket has to offer. On the practical side, there is one of the nicest laundry facilities you will find on one of the docks (rolls of quarters are available from the Harbormaster's office). There is a fine ships chandlery at the foot of another dock and the Grand Union supermarket is across the street. There are also plenty of well-maintained showers and bathroom facilities on the docks. Pump put is in your slip (arranged through the harbormasters' office), free but a tip is expected. The Concierge office has lots of information on bike, moped, kayak and other small boat rentals. They will also help with restaurant recommendations and reservations.
I've gone on far too long. I'll let some others give restaurant recommendations and such although I will mention that there is a restaurant on the docks, Slip 14, which does a killer soft shell crab sandwich at lunch.
All the best,
If you have friends or family that want to visit you but no room on board there are also cottages on the docks for rent. Again, not cheap but they are very nice and the Cottages people will work with the marina people to put you as close together (or far apart) as you like.