There are a few different options that you might consider in Huntington. The 21 Club at the Frederick is a little more upscale but not as much as Savannah's. I've not eaten there yet myself but I've heard that it's good. I'd imagine you could walk in wearing Khaki's or jeans with a nice shirt and be just fine. It's located in the Frederick building on 4th.
21 at The Frederick
Another option is Fat Patty's. It's located on 3rd ave across 20th St from the stadium. It's a more relaxed atmosphere but still has a bar and the food is great.
Fat Patty's - Home
If you are looking more for a bar/hangout with food, then you might consider Hank's Wallstreet Tavern and Piano Bar or the Union Pub and Grille. I've never been to either of these but have heard most people like them and that they are more of an adult hangout. St. Mark's on 4th, right beside the Frederick, is also supposedly a good hangout as well.
The Union Pub in Grill - Huntington, WV - Whrrl
It's not open yet but Huntington Prime might be a place for you to consider in the future as well.
Huntington Prime
Hope this helps.
Tim