As to what area of the city, I'd say Sukhumvit area. I am currently at soi 8, a place called Adelphi Suites. I have stayed at this place now for at least 3 years on every trip to Bangkok. I'm in the biggest apartment, which costs me just over $100 per night, but you can get a studio for maybe $60. It includes a decent breakfast. Location is about 2 minutes walk from NANA skytrain escalator (the escalator is a lifesaver!!!).

Leaving for HKG for a few days, but will be returning to soi 8 on Thursday. I will be checking out just as the OP is arriving! Too bad!

Have a great time in BKK. Its' currently very hot and humid (a downpour is happening right now as I'm packing for HKG trip)