What cruise line and exactly how small is the ship? I gravitate towards river cruisers as a criteria for small, that is around 150 passengers. I just knocked around and suspect you will be traveling American Cruise Lines, maybe on a ship with a passenger load down around 100.
As to that time of year, just plan on bringing rain gear so you can do one of the excursions even if the weather is imperfect. You will be docked near some of the better areas to poke around anyway, so figure a lot will be done on foot. You are likely to be a bit south of the wetter weather that Maine has in June.
I can’t tell you more than you can get by knocking around on the web regarding the places you will be visiting. I suggest taking full advantage of any on-board experts in the local area and seeing if they have devices to get you out on a self-guided tour - many of these cruises do now - so you can just go out and explore yourself. Many of these devices now also have some GPS built in, so if your smart phone is out of juice the tour unit can get you back to the ship.
I looked at the amenities and even if I got the wrong line and ship it looks pretty similar to river cruisers. A good company will make it pretty brainless to enjoy yourself in unfamiliar places. For ex on river cruises guests generally check out and in again from guided excursions. So if someone has gone missing or is inexplicably late they know.
The ships tend to reposition at night so guests have a full day at the places to visit. Leave in the morning, back by dinner time and the ship often takes off during dinner. This is not a problem - any decent line is falling all over itself trying to have better food than the other guys. You will not be hungry or feel poorly served unless one of you is on an extremely limited diet. For insomniacs like me, night time travel is a nice opportunity to hang out in the lounge or on your balcony and watch the lights go by at some wee hour.
If you have guided tours keep some singles in your pocket to tip the guides. They are often local folks with whom the cruise company contracts, and don’t get tips from the cruise line. Tips on these cruises are variable, your cruise line may include them or they may be separate. Look around on the web site or at the more detailed materials you have been sent, tip guidelines for on-board staff are always included.
This is a very easy way to travel, and you will find that small ship cruisers are an easy bunch. It is a different decision than big ship cruises and passengers expect to interact with new people. The floating cities have lots of programming that makes it is optional to actually get to know your fellow passengers.
I don’t know anyone who has tried a small ship cruise like this and not loved it, except for one person who really is a big ship kind of guy and tried it as an experiment. His instincts were correct, he liked it but didn’t love it compared to the 24 hour partying of the floating cities.