I've stayed in the IC and the HI and live in NOLA:

The IC is perfect for someone who is working downtown, not so good for tourists (generally, its great for Mardi Gras) -- its a long lonely walk from the IC to the french quarter late at night. The IC is a business hotel IMHO, not a resort / vacation hotel. The restaurant is good and Luke accross the street is excellent.

The HI is a perfect location, quiet, and has a nice courtyard / pool. If they think their going to be in the quarter most of the trip, this is the place.

I would probably pick the Hotel Modern over the Indigo -- they are both new, but the Modern is closer to the Quarter and Frenchman -- both would require a cab.

Finally, I would stay at the Crowne Plaza. Nice pool, room service which might be nice on a honeymoon, good restaurant. Also an excellent location.