Try calling around to places like George and the Dragon and Best of British, the drinks won't be as cheap but you may be in good company with other Mags.
The Ale House is about as American as you can get though which I know is always a treat for tourists. Do yourself a favor and get the Zingers - or if you're feeling particularly gluttonous, get the Zingers Mountain Melt. And the Capn'Jacks Buried Treasure for desert, it's incredible.
like you say it being very American does have a nice charm to it.