We didn't go to the Superdome for a specific event, so my experience is probably not typical. We just wanted to check out the dome and eat. We were only in town for 2 days/1 night.
Before we parked, we asked if we could go inside, if the restaurant was open, and if there was a gift shop. The lady in the booth couldn't put down her phone while she answered us, but she did tell us that "yeah, you can go in, they got places to eat, you can walk all around, and there's some stores."
We paid to park, then walked up to the entrance. The doors were all closed and covered. We must have looked confused because a nearby group of guys informed us that nothing opened until 2:30 p.m. It was just after 11. So, annoyed that we had been told "yeah, we could walk in and do whatever" by one person that worked there, while it was obviously closed, we decided to at least walk around it, since we'd paid to park.
We made it half way around the building, and my guy asked at a ticket window about going inside and if there was a gift shop. She told us that you have to have a ticket to go inside (totally makes sense) and that the gift shop was open 11 to 3. So he asked about the restaurant, and she said it opened at 1.
We finally found the gift shop. By that point we were fairly frustrated with the constant different information and just left.
I'm sure if we went to a game, it would have been great. But you would think that people could be a little more helpful at such a major tourist attraction! We were extremely disappointed, and that never would have happened if the first employee had told us that nothing would open for 3 hours. We could've left, come back, and thoroughly enjoyed ourselves.