From New Orleans I can highly recommend you take US90 rather than I-10, and then US19/27 out of Tallahassee. The former being a great drive along the beach. US19/27 is virtually interstate standard. It is a very pleasant scenic drive. I have only taken it as far as Ocala, but there is no reason to believe it would be any less enjoyable/scenic into the Tampa area. If your girlfriend is interested there is a quilt museum along that route.... somewhere around Chiefland, if I am not mistaken.
Further south you have two options to cut accross Florida. There is Alligator Alley, which is a toll road, and there is the Tamiami Trail - US41. This takes you through the Everglades, although not the national park. The short detour on route 94 has a real Everglades feel to it. US-41 also passes through Big Cypress national preserve, the refuge of the last 120 or so, panthers in FL. Tours are held regularly, and if you're lucky you might get to see a panther in the wild.
Both have a lot to recommend them, it all depends on what interests you most.
Lifey