They spent 10 episodes (over what I assume was several months) going from Chicago to Philadelphia, which is about 800 miles. They spent 10 minutes going from Philadelphia to Atlanta, which is also about 800 miles.
The nuclear bomb subplot should have lasted until the rest of the season. Terrible writing on their part that it's over in a single week. Not to mention the Georgia Federation is a heck of a lot more interesting to me than the Monroe Republic. It's obvious that conditions are so shitty in Monrovia because Monroe is a dick and keeps the peasants down.
I suppose at some point off-screen Miles, Charlie and Nora could have hitched a ride on a steam-powered passenger bus or even a steam passenger train. Assuming that, unlike the Monroe Republic, the Georgia Federation has an organized intercity steam bus and train transit system for civilian passenger travel.