Elliott Key, ocean side of Biscayne Bay, has beaches and docks and campground and bathrooms and nature trail.
Just south of Card Sound Bridge you could take a right and sail up the canal to Alabama Jack's and tie up to their dock for lunch.
You can anchor almost anywhere around the fringe of Card and Barnes Sounds (except for the north end of Key Largo where the Ocean Reef community is, because they probably would not like you anchoring there). But if you anchor, you should pick a lee shore to reduce mosquito problems -- mostly mangroves.
There are three parks at the south end of Biscayne Bay on the mainland side, and I don't know for sure what facilities they have.
If you post this question on the CABB forum, maybe some local sailors have more information.
Sorry. I keep meaning to investigate all these places, but just haven't gotten around to it yet. Maybe when we get back down to Florida in the fall.
Maybe you can do the exploring and let the rest of us know what you find out.
Not much in Key Largo, although you can anchor your boat right next to shore at America Outdoors Campground.