Okay, I've lived here in N.O. my entire life and I really don't like to say anything bad about staying anywhere in the French Quarter.
BUT, to be totally honest...... that hotel you're talking about is not in the best location. It's in the FQ, yes, but it's on the western perimeter and adjacent to a rough area of town. It's not someplace I'd suggest to make a reservation at.
Although, the property may be a nice place, it's just too close to a bad area of town.
So, no....don't stay there if you're concerned about walking to, and from, your hotel at night. During the day....it's fine, but at night it's something completely different.

Suggestions: It seems like you may be rate concious, so look into the Ramada Inn on Bourbon St, Holiday Inn FQ or some of the hotels that buy advertising on Tripsmarter.com. They really do offer some great deals!
I actually lived (briefly) and worked about 1 block from that Rampart St. Hotel and it's an area with lots of character. But, it's just not the best option for someone who really wants to experience the FQ and the wonderful amenities it has to offer a first time visitor.
Good luck on your trip and please let me know if you want some more advise.
-Gene