Mid week or weekend?
Depending on how close to the city you need to be and whether or not you have a car you might consider the Marriott at Lakeway Plaza.
http://www.marriott.com/hotels/travel/msymm-new-orleans-marriott-metairie-at-lakeway/
I apologize for the quick edits with paint, but it might help put it into context. The hotel is in Metairie which is about 7 miles from the downtown / central business district area.
The reason I suggest staying here is the hotel has a nice fitness center with virtually brand new equipment if you need a treadmill, they offer spin classes as well if you want to ride. There is a path that runs along the lake that offers plenty of room to run if you want to go outside and if you have a car you’re about 7 miles from the UNO Lakefront Arena which has an indoor pool for use as well.
The star on the map is an area where traithletes will often get in OWS during mid week afternoons that portion of road is part of the run course for NOLA 70.3.
