Finally a way to turn off LTE for the Galaxy S3! (Saves a lot of Battery)
Got this from another forum and it seems to work!
1) With phone on, take off back cover and press your SIM card so it releases from the spring. It won't come all the way out as it's blocked by the battery. This seems fine - I didn't bother trying to force it out as I didn't want to break anything...
2) Once you see the message that the SIM card is removed, go to the dialer and dial *#2263#
3) You should see a menu with band selections. The current setting is "Automatic". If you switch to "GSM All", you will be EDGE (2G). If you switch to "WCDMA All", you will be on HSPA+ (3G, though AT&T and others call it 4G).
4) Press the SIM card back into place until it clicks. For whatever reason the phone will not recognize it until you reboot. Upon reboot you should see your new setting in effect.
Idk why they don't just make a toggle for this like the iPhoen 5 has, but this is an alternative method which seems to work! I have tried