Don't know about the cheapest, but Fat Tuesdays is right by what used to be the pier. There was a little bar across from Fat Tuesdays that had reasonable beer. Have a great trip!!
playa mia is great if you like sun, sand, and surf with your drinks. A little advice - 1st time at the bar- give the bar tender a ten and you will get the good stuff the rest of the day instead of the stuff that will eat a hole in a syrofoam cup.