The fog is the worst in July and August. Why do I say that in contradiction to the previous post? Well I have lived on Mount Desert Island for the last 19 years and see the weather here every day. Fog can be an issue if you are not familiar with it and radar is nice to have. However, once you get east of Penobscot Bay there is much less traffic (virtually no commercial ship traffic), particularly on foggy days. A piece of advice if you do run in the fog - Do NOT put your marks on top of buoys. Many people do that and it results in lots of traffic right around buoys. Put your marks a couple of hundred yards from buoys and you will be much happier and will encounter fewer other boats. Judge how far off you set your marks based on the actual visibility.
We are in a foggy stretch right now, but the fog generally lifts by noon and you will have 4-5 hours before it comes in again. Also, the fog generally dries up in the lee of islands and places like Eggemoggin Reach are much less foggy than further out.
As far as getting "stuck" someplace like Frenchboro is concerned, the lobster gear is much more of a hazard than the fog. Look at your charts and choose waypoints well clear of the hazards and you will be fine. For reference I have run from Frenchboro to Mount Desert Island in the fog quite a few times.
As far as when to cruise Maine. I like June the best because the lobster gear is mostly out in deep water until after June 20 or so - i.e., you won't see as much gear inshore where you will be running. There is also less fog. On the negative side, not everything will be open and it will be colder (lots of 50 degree days out on the water). I also like September because most of the visiting boats have gone home. There is less fog, the days are not as hot and muggy and the nights are cool. Some businesses will be closed for the season after about the 5th of September, but there will be a lot more room for visiting boats. As far as staying at docks is concerned, there are not a lot of marinas east of Portland (Robinhood, Boothbay, Rockland, Belfast, Stonington, Southwest Harbor and Northeast Harbor are pretty much it). Everywhere else you will be either on a mooring or anchored. There are few services east of Mount Desert Island.