If parking is an issue, stay at Le Richelieu; it is the only hotel in the quarter that has free onsite parking. There are no interior halls; all of the rooms open off the courtyard-side walkways. If you're there when it is warm, there is a good pool in the courtyard, too.
The boat cruise to Audubon Park is very worth it, IMO. You get a river-side view of the Port of New Orleans, which is the second-busiest freight port in the US. It's very cool to see how it all works.
Also, a note about bugs: if you cannot tolerate the thought of a roach in your room, don't stay at a small hotel with rooms off the courtyard. One or two bugs will routinely manage to get under those doors in warm weather. The only truly bug-free hotel rooms in New Orleans are the larger modern hotels that were built as hotels; if the building is converted and over 100 years old, no amount of scrubbing and spraying will eliminate them entirely.
Now if you understand that and like small hotels, I can recommend a few. For a romantic splurge, nothing beats the cottages at Maison de Ville. If you like funky and do not have any young kids with you, the upstairs rooms at the Villa Convento are very atmospheric. (VC's legend is that it was the inspiration for the House of the Rising Sun. Probably not, but it is cool to sit and look out over the rooftops in the morning. They don't allow kids under age 10.) If you want modern suite finish in an old building on the fringe of the Quarter, the Iberville Suites in the old Maison Blanche building next to the Ritz offer a lot of room to spread out.