I used to live in BKK and I have made "I cant even count" number of trips. So here goes.
1. There are plenty of malls around Sukhumvit, Silom areas. They are all connected by the metro train service.
2. Go to Chatuchak weekend market on Sunday. Its the last stop on one of the metro lines. This weekend market sells everything from furniture to exotic birds and animals. oh! yeah! remember to bargain 50% of the asked price. And its quite allright to bargain. Make sure you keep smiling.
3. You can go to the evening market near Wireless road (I forget the name) but you cant miss it. I would still prefer Chatuchak.
4. You can sign up for a day tour with one of the many tour guides. But stick to the one with the hotel you are staying. If you dont like it, you can always complain to them.
5. Floating market, the palace, the sleeping buddha, trip down the backwater river of Cho Praya, the royal barge parking area. are some of the things that can be done.
6. The sukhumvit area street shops sell cheap t-shirts and clothes. remember to bargain too.
7. If you are not into bars, then forget them. Else, for the heck of it, visit one of the girlie bars. Its a system shock but hey! its life.
8. Visit Bed Supperclub, an upmarket swanky bar. Its a cool place for seeing totally different side of BKK.
9. Get a nice massage. You can get a 2 hour massage for 600B. which is like 30SGD. And pick places which are near the shopping areas. You dont want to go to sleaze pits where they promise "happy ending". I am not kidding. You dont want to waste your time and money. You want to have a good solid and relaxing massage.
10. Visit the Patpong street 5 or 6. Its a street predominantly patronized by gays. But the restuarants there serve top notch food. The thai food especially is extremely tasty and good. Since you are a girl, you would be fawned over and spoilt like a princess. Once again, trust me! my ex loved it and I was the one squirming.

But after 10-15 minutes you relax because its all very clean and safe.
Hope this helps a bit!