I'll third the local game store optionas the best one you can find. Most of them *love* hosting gaming groups, because it's a strong incentive for the gamers to purchase stuff there and earns them good will in the community... Plus it gives them a chance to cross-sell other games to your group. The biggest catch you'll usually have is that a growing number of them don't want you to bring food - they want you to buy from the store. If you go this route and order pizza, seriously consider ordering pizza for the staff as well.
1) Libraries. Some may go "OMG, devil worshipping RPGers!", and some may just not have a convenient room to play in, but some have study/group rooms you can schedule or rent. Plus, if you have a good library, they'll stock the game-books and novels for you.
Downside, they're usually tough on food.
2) Schools. High schools are much touchier now, but colleges frequently have gaming clubs and libraries and student centers that may be options. Downside, it's frequently much harder to get access if you aren't a student there.
3) Community rooms. In Schenectady, NY, the local war-gaming club meets at the Price Chopper (a supermarket) Community Center, for a very reasonable amount of rent. Malls, department stores, and restaurants occasionally have similar things. You may have to dig a little, but they're out there.
4) Restaurants. This sounds weird, but I did it in college for about two years with some friends. Find a 24-hour diner, or a restaurant that's not busy certain days; make friends with the owners; and say "Look, I have a group of guys who want to get together once a week. We'll be talking, but we won't be disruptive; if we buy dinner and drinks, can we snag an extra table for space and hang out in the corner for a few hours?" On a Saturday night, they'll all say "no!" (they want the space, and they want people to move through quicker), but on a less busy night they might well say yes. Just remember they're a business, and be respectful and buy food and TIP WELL.
