Don't know about cab pricing. You are not really very far from the city, but lots of stop and go traffic, especially any time near rush hour. That would add to the taxi cost. You would have to call for a taxi to pick you up at the battlefield, but I think any cab driver would be happy to do it because you would generate a respectable fare and they would end up in the city where they could pick up a new passenger. You would get to see a lot of old New Orleans residential architecture on the way back to the city. Not mansions, but middle class housing probably built between the Civil War and the turn of the 1800-1900 century.

As everyone else replied, the park is up and running. It has a wonderful free museum and the locals love to walk, run, or bike around the battlefield. It has restrooms and I was even able to go up into the monument for the very first time this past Battle of New Orleans Celebration (always second weekend of January). The monument was 102 steps up and boy did my legs suffer for it the rest of the week! I was so surprised because I walk 5 miles all the time! If you visit the battlefield by car, be sure to eat at Rocky and Carlos, they have great Shrimp Po Boys and Old Arabi Grocers has the best Roast Beef Po Boy and Muffelatta. But yes, you are right, St Bernard took a huge hit after Katrina and many areas got over 9 ft of water. The good news is that Old Arabi just opened a lovely science center in a renovated Old School Bldg, it even has a planetarium! It's on Friscoville Drive.