With a 3' draft, you might want to consider staying along the
ICW and not going on the ocean through Hawk Channel. There are just more options on the
ICW side.
If you really are meaning to stay in Hawk Channel, there are a few OK
anchorages - nothing more than a place to spend the night and go in the morning:
Tavernier Key, Rodriguez Key, and Pennekamp is a standout apart from the anchorages on that side. They have moorings you can get to too.
Pennekamp is probably the nicest thing to do from that side with your draft. Check out all of the things on the bay side though. Depending where you are, there are multiple places to cut over.