The Old Fort and Hudson's are reputed to be very nice.
We like Kamura's Steak House, for Japaneese style cooking at the table where you sit.
Many will recommend the Old Oyster Factory.
For an upscale lunch, go down to Harbour Town and eat at the golf club - public welcome.
Sue and I like Kingfishers, but some others don't for various reasons. We had a great meal there following our wedding and they have a great "romantic" atmosphere with the live music.