We have stayed at Richelieu. It's got a nice New Orleans flavor and is near the French Market and Jackson Square. It felt like a LONG way to walk after a Bourbon Street binge, though!
At the time you're going, you should be able to find lots of options at that rate, especially in the Central Business District, the neighborhood next to the French Quarter.
The closer you are to Canal St., the shorter your walk to the FQ will be. Le Pavillon is about a 10 minute walk to Canal, but it's a gorgeous historic hotel that offers guests a free nightly hot chocolate and PBJ buffet--very charming.
Best Western St. Christopher is another unexpected charmer. Sounds like a generic chain, but our room was huge with exposed brick walls and a view of the river--and that was the budget option.
The Sheraton on Canal is less charming, but they have reasonable rates, and it's just across the street from the French Quarter.
If you want to stay in the French Quarter, you'll have shorter walks to attractions, more historic charm, but pay more. Le Richeliu is a good option, and so is Dauphine Orleans--both should be in your budget range.