Savannah
The Rock and Roll Marathon is coming to the coast!
When to come?: 

Savannah is perfect in winter - soft breezes, humidity from the ocean, warm weather. Spring and fall are nice too, but skip summer if you want to gt your long runs in without melting.

Where can I go to get out away from the city, without driving too far?: 

Skidaway Island State Park is only 15 miles southeast of the city, and it's a really nice getaway for camping, hiking or mountain biking.

What mountains/hills can I hike nearby?: 

There are no real hills or mountains anywhere near Savannah - just low marshes, woods, and grasslands. You'd have to drive about 5 hours to the Appalachians to do any real mountain hikes, though it certainly does get hillier further inland in Georgia

What outdoorsy stuff is way overrated in this town?: 

Running through Forsyth Park looks like it might be fun, but it's not that big - do it once or twice, or maybe make it part of a run through the whole historic district.