Tamara is correct.
It could possibly be that the Network Towers in the areas are busy with lots of data traffic and have a delay. But a couple things I would like you to try out.
1. See if the Delay occurs in other areas then at home, Like at work, around town, other cities etc.
2. Reboot the iPhone and see if the delay continues, Hold down the Home button & Sleep/Lock button together, Let go once you see the silver Apple Logo. iPhone OS will reboot.
3. Toggle Airplane Mode on for 1 min, Settings-Airplane Mode ON for 1 min then Turn OFF, Now test SMS
4. Reset Network Settings - Be advised if you setup VPN, and or programmed WiFi passwords, These will be reset and need to be set back up when the time comes for that. Settings- General - Reset- Reset Network Settings - Confirm - iPhone will reboot - Retest SMS
Removing SIM card
http://docs.info.apple.com/article.html?artnum=305746
5. If needed Eject SIM card from iPhone clean it with a soft cloth that is dry, Blow gently into the SIM card slot of the iPhone to blow out any small particles, Now put SIM card back into tray and back into iPhone, Test SMS
6. Contact AT&T for further assistance with this issue. Refer to department that assists with EDGE Data