Good idea. We've sailed into many harbors on the East Coast of the US from Canada to the Exumas over a few decades, and the really handy ones-to provision, ease of shore access, etc., are not that easy to find. We've sailed for a couple decades with kids of all ages, and know what a find a good provisioning stop is, especially for a family.
On the coast of Maine in Penobscot Bay in particular, Camden Harbor gets my best rating for all of the above. All the regulars like Diesel, gas, LPG(filling all sized tanks), CNG exchange(both small and large bottles), ice(even 50 pound blocks!), are all available from dinghy docks around the harbor.
Chandlery(medium sized but ample for 90% of what a transiting boat would need) at Wayfarer, on the water.
Provisioning; steps off the public dinghy dock, French and Brawn is a full service grocery, with butcher shop, fish monger. Not the big box grocery store but a real find for a boat with a hungry crew. The kids will roll your cart to the dock, unload and take you back(or call the water taxi).
Full drug store, restaurants, book stores(marine/chart heavy), second to none public library on the harbor(free wifi), Vespa rentals, you name it. It's a busy harbor with a lot of tourist traffic onshore in summer.
The biggest drawback is, the anchorage is exposed to the south and at times, choppy but there's usually plenty of space to drop the hook. Moorings are almost always available with showers, laundry, taxi etc.
Dockspace in the inner harbor is available but usually taken and expensive. The best find is an inner harbor float(check for an overnight rental). Private, dead calm protection, easy dinghy row and quieter than the town or marina docks.
The town docks are reasonable if you can find an overnight space, and they'll let you tie up for free for a couple hours to provision. Great anchorages(like Pulpit Harbor, Fox Island Thoroughfare) are just an hour or so away.
Next best I think(only second because of location up the bay), is Belfast for ease of all the above.
For full chandlery, Rockland has a Hamilton Marine right on the public pier. Everything is available in Rockland, but you have a schlep to a big grocery store.