IPhone – Is the iPhone 5s Voice over LTE (VoLTE) capable

Not much in the way of a major community database of real-world speeds, sadly. Here are some other resources:

1. Verizon's LTE coverage map
2. AT&T's HSPA+ coverage map (and overview)
3. Overview of all major carriers, and another (older)
4. More general information on current/planned deployments
5. Verizon coverage map with speed tests - Minneapolis/St. Paul area only.

You might also use the FCC's GIS data to find out more about what towers already exist. Presumably, they're not going to build new towers for LTE - just add antennae to existing sites.

The LTE toggle shows up when your carrier settings indicate LTE is available for your device.

If you have data, you can update OTA by going to Settings > General > About and waiting (or tapping on your current carrier settings to see the details).

A tethered check is also available by connecting your iPhone to iTunes and checking for an updated carrier profile for your provider. If there isn't, the most likely explanation is that your provider has not enabled LTE in their carrier settings. If so, contact your provider on whether any LTE (even if not theirs) will work on your iPhone.