First of all, you can generally get a NICE room on Priceline or Hotwire for the price of a Red Roof room. See
http://p070.ezboard.com/fpricelineandexpediabiddingstlouis for more information. When I head to St. Louis, I generally pay under $45 for a Courtyard by Marriott or Doubletree.
As for specific areas, the areas that generally appeal to the tourist trade include the downtown area, Westport, Chesterfield and Clayton. Each of the areas has its plusses and minuses.
Downtown is the most convenient. However, many properties charge for parking and the rates tend to be higher. Also, you have to be more aware of the environment as it is not crimef-free but it is not too bad either. My low-cost recommendation is one of teh Drury Inns. The one across from the Union Station is a historical landmark and a must see for the architecture.
Westport is further out but has a ton of hotels that do not generally fill up on weekends (except for Cubs-Cardinal weekends). They have more shopping opportunities and some nightlife. It is less convenient to the Arch and other areas around town.
Chesterfield is further out from town BUT the area has more of a rural feel. The Doubletree Conference Center is pretty cheap on weekend and is usually a favorite on Priceline. The problem with this area is that it is not close to anything.
Clayton has a lot of entertainment and a lot of good restaurants. It is a walkable neighborhood and a well-kept area. Think a more urbanized Lake Forest. The hotel inventory is fairly limited, especially in the budget category.
The cheapest area of St. Louis is the airport area. However, the area around the airport is a bit on the rough side. I generally stay in that area when I travel to St. Louis on business. It is OK if you are driving BUT not an area that you'll want to walk around.
(Disclaimer: I was a night manager for one of the Westport properties 15 years ago.)
Hope that helps. PM me if you want some Priceline advice or if you have trouble finding a place on a busy weekend.