If you're googling for rooms to check out, make sure you call ahead. Lot's of places have closed or severely restricted hours: Willie Mosconi Recreation Center, Broad Street Billiards, and Viet Vuong are all shuttered.
Drexeline is definitely worth stopping in; imho it's one of the best rooms on the East coast. I'd caution you, though, that you're going to spend at least 30-45 minutes in a car getting there from where you're staying. Tacony Billiards and Ballbusters are also accessible by car, and while they aren't quite as notable, they still attract good players and would be more convenient, geographically. (The standard I'm judging by, here, is that more often than not you'll walk in to find a game of straight pool going on at any of these three places. Drexeline is a destination while Ballbusters and Talcony Billiards are pool halls you'd find anywhere in the country.)
Your only option within walking distance of downtown is Buffalo Billiards in Old City; it's pricey ($12 an hr?) with tired Brunswick tables that have generous pockets. Not really a players spot but you don't have many other choices in the area, unfortunately. It's not a bad place to relax and you can't beat the location.
If you don't mind a dive bar with a small table to match, Tops on 15th (above a bar called McGlinchey's) could be an option. APA plays there and I find I can almost always get a game later at night. There's also a spot on South St. called Tattooed Moms that has a really active bar table if you're comfortable with an under 30 punk rock styled crowd.
On Sundays, there's a bar called the Green Room in Fairmount that offers free pool with cheap pitchers. No real players, but another good place to get a game for drinks.
And last but not least, my favorite: The Russian Ukranian Boating Association (aka Ruba Hall) in Northern Liberties. Free table, cheap drinks, always an adventure. They'll sign you up as a lifetime member for $10. Neighborhood gets a little sketchy after dark, but that's exactly why you'd go.
Philly isn't unsafe. You won't wind up going west or north enough to really have an issue. If you are driving, though, don't leave anything visible in the car when parked on the street. Windows get broken for a few cents, let alone an ipod, bottle of wine, cd collection, or dare I say it... a pool cue. If you do wind up going to Deptford, careful you don't get lost in Gloucester or Camden– after dark, heroin traffic is so bad there that if you have out of state tags, the police are likely to stop you just to make sure you know the quickest way home. I'd also advise that the drive to Deptford is long and takes you through some of the worst scenery (and traffic) South Jersey has to offer, though I'm sure the tourney would be worth the effort.
Good luck and have a great time; it's an amazing city.