Baan Chart Hotel
Here's a short list of hotels offering good rates for high quality rooms. Depending on exchange rates, these may cost you a bit more than $50, but they'll still give you good value for money. The locations may be a bit away from the center of things, but all of these selections are within a minute or two walk of the Skytrain or subway. You can also simply go to Agoda and get the best rates on any Bangkok hotel.
One other cheap option that is close to the center of things is the Red Planet Hotel Asoke. Red Planet is a chain of cut-price hotels once affiliated with Southeast Asia's largest low cost carrier, Air Asia.