Best places to meet girls in Bangkok in my opinion are as follows:There's Speed dating in Thailand - Easy way to get to know nice cute girls face to face and they're cheap too!
Night clubs, except after hours clubs or those in Sukhumvit area. (Full of bargirls)
BTS - They are shy in the BTS and MRT however but they might give decent eye contact there as they're "stuck" with you for a while.
Any popular shopping mall.
Thai universities. The campuses can be huge. Unfortunately not many students around now during Thai hot season/summer.
City buses? You'd be the only farang using the bus and might just get some attention! Good luck, see you in the middle of nowhere!
Special events that you can find out about on Facebook.