Am I yonsei?

Okay so, my great-grandmother and my grandfather were both born in Japan and immigrated here together. My great-grandmother is full japanese, while my grandfather is half. What does this make me, regarding japanese generational terms?

Yes, you'd most likely be considered yonsei. Nisei refers to someone with Japanese ethnicity who was born outside Japan, but whose parent/parents was/were born in Japan. The "ni" part of nisei means "two," so since you're two generations further down the family tree, you'd be yonsei (since "yon" means "four").

However, you mention that your great-grandmother is Japanese and your grandfather is half-Japanese. How much Japanese ethnicity you have from the rest of your great-grandparents, grandparents, or parents may possibly affect whether or not other people consider you yonsei, or simple a person with Japanese heritage but no particular term/title for it.

It's also worth noting that the terms nisei, sansei, and yonsei aren't actually used by people in Japan. Instead, citizens of other countries with Japanese heritage are called "nikkei" plus the term for people of their country. So, for example, an American citizen of Japanese descent would be "nikkei America-jin." Generally no mention is made of how many generations it has been since the family lived in Japan.

Well, technically speaking you're one-fourth yonsei, but that doesn't matter. If you just say that your great-grandmother came from Japan, people would get the picture. And if you want, you can go on and start a nice conversation about your whole family.

Technically, you are 4-sei, but people don't seem count after 3-sei.
There is even a restaurant named Sansei in Hawaii, but I have never heard of the term yon-sei in Hawaii.

it is the counting system of generation.
from your grandparents, you are the third generation, i.e. san-sei, san-sedai-me.
form your great grandparents, you are the fourth generation, i.e. yon-sei, youn-sedai-me.

on the basis of Japanese blood origin,
your great grandparents are Japanese. your grandparents are partly Japanese, the second generation. your parents are partly Japanese, the third generation. you are the fourth generation.

on the basis of immigration matter,
your grandparents began to immigrate to your country, the first generation. you are the third generation.

You must be 3.5 sei.

Yes, basically. If you have childen, they might be be considered Gosei, though that term is rarely ever used.