Nantucket boat basin is great. Depending on your fuel tanks, fuel up in Montauk/stay over at the Montauk Yacht Club, fuel up in Edgartown/stay over night wherever you can there, then run to Nantucket with full tanks.
We were fogged into Nantucket for about three days, had to run five to seven foot seas to get back. We passed a 40 + foot sloop that was pitch poling so violently I was amazed anyone could stay on it. We sustained a fair bit of damage also. Wires pulling out of switches, trim tabs failing etc. It was a good thing Bob was not trying to stay with us in his bowrider.
What I am trying to say is leave a window of several days if possible before and after your planned Nantucket arrival/departure dates. The comments about going to Block must be raised to the power of 5 when going to Nantucket. Hence waiting in Edgartown for good weather to run over to Nantucket is a good plan.
You don't want to get fuel in Nantucket, because the big super yachts will sometimes hog the fuel dock for a LONG time to fill their tanks. Same deal for Block, no superyachts, but just super busy. Montauk is really good to zip into for fuel, and zip out. Edgartown can be a long wait for fuel also. Oakbluffs in MV is probably faster to get fuel, but not as well situated as Edgartown to sit and wait for good weather.