Umm…to answer this question, I have to tell you first that you can shop anywhere in Bangkok. I literally mean it. You will find markets and shopping malls all over the city, and many of them are located next to the BTS Skytrain and MRT Subway. So, my recommendations are
Stay close to BTS Skytrain or MRT Subway
The word ‘close’ for me means less than 10-minute walk to the BTS Skytrain. Since Bangkok is usually hot and humid, I think you would not want to take a long walk during your stay, especially when carrying many bags back from the shopping malls or markets. Besides, what you might not know is many streets in Bangkok are not good for walking. The popular shopping area is Siam Square. It would be good, if you can find a place in that area within your budget.
Stay a little far from the shopping center, but still close to BTS Skytrain or MRT
If you cannot find a place that in the heart of shopping area, I recommend you to try to find a place that is little far from the city center, but still close to BTS Skytrain or MRT such as on Sukhumvit Road. Onnut area (Sukhumvit Soi 81) is an upcoming popular area for tourists. I always see many foreigners here (I am living in this area). It takes only 15 minutes by BTS Skytrain from Onnut Station to Siam Station, and I believe that the accommodation prices in this area are lower than the ones in the shopping area. If you love tranquil place, you will love this area.
In short, the area is not that important, just stay close to BTS Skytrain or MRT Subway!
Hope this information helps.