Another hotel to consider: The CY is very close to
Lumpini Park which is a tourist spot on its own and has running paths. You will get a feel for the city and there are a few tourist spots very close, like the malls that were mentioned earlier and Erawan Shrine. The CY is a bargain, breakfast in the restaurant is quite good and free for Plats and higher; there is also a CL if you are eligible. Since you seem to need the room just for sleeping more than a fancy, elegant hotel it would seem an excellent choice. There are two BTS stations which are easy to get to and the hotel runs a shuttle if you don't want to walk.