Sandy Point State Park has a fairly decent beach but no tiki bar. I think there are a few public beaches in the Edgewater area as well. Chesapeake Beach or North Beach might fit the bill. Haven't been to either in years so not sure what they are like now. I know there has been alot of developemnt in those areas.

http://www.baydreaming.com/chesbeach.htm

http://www.chesapeake-beach.md.us/