Smyrna is hot and for good reason. It is convenient, appreciating quickly and has loads of shopping, dining, recreation and entertainment options.
There are 69 properties between $350 - $400k on the market in the Smyrna area. Of those, 29 are under contract. So, yes, they do go quickly. My buyer clients are not limited to what is listed, since I have means of giving them access to homes that have not yet on the market. And I get them through the door quickly so that they have a chance at their dream home when it becomes available.
In addition to Smyna, You may want to consider the Covered Bridge area of Mableton as well as Mableton's Southeastern edge. The neighborhoods mentioned - Ennisbrook, Wetherbrooke, Woodland Brooke, Woodlands Highlands are all good. Also consider Barnes Mill, Legacy at the Riverline, Smyrna Heights, Medlin Park, Woodbridge Crossing, King Valley, Chapel Hill at Vinings, Vinings Estates, and Providence.
I hope that this helps. Good luck. Please check out my Trulia profile and contact me if you would like an aggressive agent to help you get into the right home.