Well I'm from that area, so I never stayed in hotels, but here's what I can recall.
I've wanted to stay in Hotel Monteleone. It's in the quarter but I think rather expensive.
There is a Westin that is very nice and in an open area. It is in the Canal Place (mall) building, and I used to park in their parking garage whenever I would drive down to the quarter by myself, so I've felt very safe there (well as safe as you can feel in the city). It's right by the river.
I stayed at a Ramada hotel once when I locked my keys in the car in that Westin parking lot. It was less expensive but still very nice and close.
There's a big Days Inn on Canal where a lot of the parades go. I've stood outside that hotel for parades before. It's in an open & safe area, right on the edge of the quarter.
That's all I can think of. I'm sure you can get better info from actual Mardi Gras tourists, but it's a start.
I'm planning on going this coming year too, as long as I can get off from work. Maybe we can have a Mardi Gras mini-meet! I do, however, boycott Bourbon Street during Mardi Gras. That's not my scene at all.