Mr B's on Royal Street - go at lunch time for their BBQ Shrimp - the sauce is absolutely amazing. Dinner is good too, just more expensive.
Acme Oyster bar - look for "Hollywood", he is the "Master Shucker" Here is the
link for the on-line web cam at Acme.
Pascale's Manale in the Garden District - again, for lunch. Here is that
link. Take the St. Charles Street Car to Napoleon - it's only three blocks or so from St. Charles - plus you get to see some really cool houses on the short walk. A couple blocks the other way from St. Charles will put you near a bunch of antique shops etc. A nice area to visit after lunch.
Cafe Du Monde for Beignets and coffee - have to do it. Here's that
link.
The last time we were there, the wife and I spent some time at the Greenwood Cemetery - not a tour, just the two of us. One of the locals recommended Greenwood because it would be safe - she said we would have more fun on our own than going on a cemetery tour - she was right! We took the bus or trolly - whatever it is - on Canal Street (I think) - Greenwood is at the end of the line. Here are a couple pics:
