Gyms. Coffee shops. While out shopping. Book stores.
Reasons:
Gyms: In girls magazines, the top places recommended for women to go to meet guys are mentioned, and gyms are one of those places. So if girls are going to gyms to meet guys, why not go to the gym to meet the girls that are going there to meet the guys?
Coffee Shops: It's low key. If you happen to actually meet a girl there, give her your number by writing it in her phone under the name, "Coffee Guy." Or something like that. She'll think it's cute.
While out shopping: Uhh... well, there's lots of girls. Girls love to shop. Just don't try picking up girls at lingerie shops.
Book stores: Same as coffee shops, it's low key. If you spot a girl you're interested in, you can try moving in by peeking at what books she's looking at and start up a conversation that way.
Some other suggestions...
Art exhibits
Museums
Uhhh.... yeah, that's all I got.
Very Very Helpful.