Scooter's Bike Shop
River City Cycling
The Bike Pedaler
Bikes Etc
Dick's Sporting Goods
Academy Sports & Outdoors
Your best friend
If you are new to the riding or you have not been on a bike in a few years, "it's just like riding a bike!" Besides for a bike, the most important thing when biking, WEAR A HELMET. Your head is one of the most important parts of your body, don't have Mr. Noggin meet Mr. Road. Next, always bring water when you ride. Especially if you are riding in the middle of the day or towards the evening hours. Always hydrate when you are doing physical activity.
If you are in the mindset to try and become a Thor Hushovd, current World Champion and holder of the yellow jersey following stage four of the Tour de France, here are a couple of the organizations in Ark-La-Tex that can help:
http://www.teamlasport.org/
http://www.sunrisetriclub.org/
http://www.texarkanacycling.com/
Good luck on your bicycle adventure if this is the fitness route that you choose to go. The Tour de France is currently airing in the morning from 7-10 on the Versus Network. Most of all, have fun and keep those pedals turning!