Turns out getting a hotel with parking near the French Quarter isn't all that easy, and getting parking for the Harley was a bit harder. I searched and found the Old Town Inn which, besides being a cool old place, is motorcycle-friendly and has off street parking.
This one looks homey enough that I can kick back and relax without having someone pointing fingers at that "biker guy" over in the corner. It's about 6 blocks from the French Quarter, and I scored a 2 bedroom suite for less than 100 a night, with a fridge and TV.
So now I'm thinking about having some company down that way.... New friends and old......