To avoid selection bias, I'll avoid recommending my own hometown, and instead offer: downtown Chattanooga. Located on the Tennessee River, close to the mountains, plenty of outdoor activities, city-funded broadband Internet, with a low cost of living (TN has no state income tax).
https://www.walkscore.com/TN/Chattanooga/37403
I've been looking at Chattanooga a lot lately as a relocation area for a different job. It looks pretty solid. In addition to what rubic said, the real estate looks pretty cheap, and from what I can tell, you can rent it out with no taxes other than property tax, which are very low. Also has a pretty diversified economy.
Chattanooga is gentrifying -there's still a LOT of crime around those cheap houses. So look into that carefully. People I know in Chatt would not consider living in that area - they live 15+ minutes out in the suburbs and nearby towns. TN has no income tax but they have certain taxes on investments and the sales tax is high. For people interested in traveling by air, the airport there is very small.
I live in Chattanooga, and although it is an amazing town, especially for outdoor enthusiasts, there are some downfalls. There is a decent bit of gang-related violence in parts of the city (that are relatively easy to avoid). North Chattanooga would be a great option. Very bikeable/walkable to downtown (5-15 minutes crossing over the mile-long walking bridge every day does not sound bad). However, the houses there are more expensive, as the 20-30s young business professionals have taken over.
Other than living in North Chattanooga, or an apartment downtown (again, expensive), you need a car to go anywhere else.
There is a lot of biking, hiking, watersports, etc. available for outdoor enthusiasts (I am a big trail runner and mountain biker).
Another downfall is that the school system is pretty poor. There are lots of private high schools in the area that are great, but again, very expensive.