Seconded. Rick's in the Reading Terminal Market is another good one, and there are other places scattered around town that blow Pat's and Geno's away. Of the touristy places Jim's on South Street (currently closed because of a fire that damaged it this past summer) is the best.

Also as a Philly native, I will say that while cheesesteaks are awesome, real Philadelphians know that the roast pork sandwich with sharp provolone and broccoli rabe might be even better. It's called "John's Roast Pork" and not "John's Cheesesteaks" for a reason.