Since a "cheap" hotel in some ways is subjective. Why? price versus what you have to put up with. So, even though someone recommends a place, unless they have stayed there within the last 60 days then you don't know what is really happening at any hotel. Whether its pest infestation, or remodeling or whatever. And please keep in mind, this is not like the US or Europe where someone polices the star rating. Hotels in Asia self rate. And in Asis they do use a 6 star systems so there is a wide variance on quality.
I do not stay in this area, actually I did once in 2004, at the Plaza Athenee' hotel on Wireless Road, that's a 5 star hotel, Wonderful hotel.
Nana hotel on Soi 4 is probably the best in the area. I have seen many people recommend it.
http://www.sawadee.com/hotels/bangkok.ht…
This has the best listing to see what is around that area. Watch the pricing, some of them change at 10/31/09 and some change earlier. Don't assume you are seeing their best price.
Compare what you find on Sawadee to at least the following
agoda.com
res24.com
And if you are really ambitious there is kayak.com which is a travel search engine for flights and hotels.
Good luck