We did a week at Fowey last year with our RIB, fabulous place to have a boat.
In the town on both sides there are numerous pontoons. You can tie up a small inflatable over night with no worries. There are usually lots there and have never heard of one being taken. Its great for family as they can get on and off very easily.
Alternatively, up by the car ferry, there is a small car park, where again a small boat could be left overnight, but you would need to drag or carry it up.
There are some "locals" on here who will give you better advice.