I stumbled on this thread and couldn't help but reply.
I live in Dayton, so hopefully I can help you with your planning.
You will need to rent a car. Taxi service from the airport to the museum will likely be $20-30 each way.
you can rent a car for about $30 a day from the airport. try priceline and hotwire as well.
Are you getting a car right after you arrive? then no problem with any of the shuttles to the rental car places. there are phones near the exit and they are generally there in about 15 minutes. Some rentals are available a short walk from the terminal.
I am not sure about airport hotel shuttles to the car rental, or vice versa. I would call the one you plan to stay at. Even the downtown dayton hotels have airport shuttles - and the taxi ride would be much cheaper to the museum if you choose to go that route.
It will take you about 45 minutes to get to the museum from the airport.
Traffic should not be a problem but depending on construction projects it could get nasty during rush hour.
Leaving the museum at 5pm could be a little more busy because it is near the AF base and everyone leaves work at 5pm.
You will like having a car because you will have more choices to eat. The museum cafeteria has a very nice view but the quality leaves a lot to be desired. I think it is kind of neat to eat there - but just for a snack - not a meal.
The restricted galleries operate of a first come first served sign-up basis. There is a shuttle that runs to those galleries. Bus departs museum at 10 a.m., 11 a.m., noon, 1 p.m., 2 p.m., 3 p.m. and 4 p.m. seven days a week.
Participants must attend a briefing 15 minutes before their bus departs the museum. If you are not a US citizen you have to show your passport. They are also VERY strict about cell phone use and camera use on the shuttle.
Enjoy your trip. I grew up going to the museum. Just imagine, once upon a time you could touch everything (no barricades around the planes) and drive your car on the runways to the now 'restricted' areas.