The best way to get around downtown Chattanooga during the convention is the free electric shuttle. The shuttle has a stop at the Marriott hotel which is attached to the Convention Center. Just walk down the hall, go outside and you're at the stop. Shuttles come by every few minutes and you can get on and ride.
There are two routes that stop at the Marriott, Aquarium and Choo-Choo. Aquarium takes you toward the center of town where most of the local restaurants are (along with the Aquarium, of course) and is likely the route you'll want, though if you take the wrong one, you can stay on and it'll eventually loop back around. This is a great way to get around town quickly and easily without having to worry about parking. The shuttles stop near most of the downtown hotels and can bring you to the convention each day. By the end of Nationals, most people will be veteran shuttle riders. And did we mention it's free!