Dojo.
It all depends on the studio.
dojo
When he lived in Michigan his martial art studio was called Fabiano's Karate. Now he's on the XMA Performance Team.
Unfortunately, nowhere. It was built in a studio on set.
No, it is not rare at all. Almost every small town has at least one karate studio. Most of them are Taekwondo.
karate ka
The Karate costume/uniform is called "Gi".
Karate is practiced in bare feet. The karate uniform is called a gi.
A quick internet search identified the Ultimate Martial Arts Studio and the South Georgia Karate Academy, both in Savannah. There are probably more.
It is called an obi
yea there is it is called Gin Jan Do KARATE
Karate blocks are called uke in Japanese. We pronounce it as "ooke"