We looked at many marinas earlier this Spring as we wanted to move. First suggestion is to use Marinas.com and contact as many as you can, you can search by city and the site gives good aerial photos.
The least expensive I know of is Bodkin Marina (not to be confused with Bodkin YC) located on Back Creek off the Bodkin at the mouth of the Patapsco. I know its further North than you said but not by much. Charlie is the owner, its a no frills place and not much going on. Your 4 ft draft will work fine there. I paid $1200 a year for our 37' boat back in 2005. Bodkin Marina in Pasadena, Maryland, United States
On the Rhode I found Bluewater Marina to be the cheapest, and they just put in brand new docks, other than that its pretty slim. Blue Water Marina in Edgewater, Maryland, United States
Contrary to what Jameswilson posted, I didn't find Holiday to inexpensive, perhaps I was just quoted a high price for some reason. Great spot, I would have enjoyed keeping the boat there, Holiday Hill Marina in Edgewater, Maryland, United States
Holiday Point is to exposed IMO, hence the lower prices. Holiday Point Marina in Edgewater, Maryland, United States
There was a place near Galesville that had some moorings, but I cannot find or recall what the name was, they were very inexpensive.
Get on the phone and start making some calls, good luck.