Onset harbor is probably your best bet right off the canal. Be aware a six-foot draft will be a bit dicey in much of Buzzards Bay's smaller harbors and anchorages. A better choice would be to go out a bit further and head over to Bassetts Island on the eastern side of Buzzards Bay, in Pocasset/RedBrook harbor.
Another good stop would be Tarpaulin Cove on the southeast side of Nashuon, one of the Elizabeth Islands. Tarpaulin Cove is a good choice if the wind is out of the north or west, horrible if it is out of the south or east.
A bit further out, Cuttyhunk Harbor is fairly well protected from the southwestly to easterly winds. A bit less well protected from others, especially a northwest wind. Cuttyhunk Pond is very well protected, but fills up very quickly in the summertime.
If the wind is from the southwest through eastern directions, Menemsha Bight, outside of Menemsha harbor proper is a pretty good anchorage. It is totally unprotected to the northerly winds though.
If you're going through Woods Hole, Hadley Harbor is fairly well sheltered. South of Bull Island should be okay for a boat with your draft. Personally, I wouldn't go through Wood's Hole. The amount of traffic and the relatively strong currents can make it a PITA. I would go further out along the Elizabeth Islands and cut through Quicks Hole instead.
Lake Tashmoo might be a bit tight for you, but once you're in, the southern end of the lake should be okay. Vineyard Haven is easier to get in and out of, but you do have to contend with the ferry traffic there.
Edgartown Harbor is good if the wind is out of the south or west. If the wind is out of the north, you'd probably want to go into Cape Poge Bay, on the eastern side of Edgartown harbor. Again, your draft will be an issue in some spots.
Nantucket harbor can be a problem with your draft, especially if you're anchoring further in on the eastern side... where shoaling is an issue.
Southern side of Cape Cod can be a nasty lee shore in a SW wind. Also, many of the harbors are going to have issues with your draft.
Don't know what fees are like this year...but I've heard Nantucket is charging an arm and a leg...