"Get in" or "Get into" is a common idiom when you are placing yourself inside some more-or-less enclosed, approximately person-sized compartment such as a car, phone booth, or boat. (See also In vs. On for vehicles.) This usage is more focused on the end result of you being inside something.
"Get into" (but not "get in") is also a common idiom when you have to expend some unusual effort to cross a border or pass some barrier to normal entry. This usage is more focused on the actual crossing of the boundary/barrier instead of the end result.
"I got into Mexico by paying off the crossing guard"
"I didn't have my key, but I got into my house anyway by climbing through a window."
Barring unusual circumstances, though, the normal expression for entering a larger area like a city, state, or country is simply "go to", which places the focus on the time spent at the destination:
When I went to Japan, I ate nothing but ahi tuna the entire time.
Although, if the focus of the statement is on the actual arrival itself, "get to" can also be used:
When I got to Japan, I was so jetlagged that I couldn't even read the signs that were in English.
So, to answer your question directly, because Japan is not a more-or-less-enclosed compartment of approximately person size, we don't generally use "into" when referring to our arrival there.
You will also find "get into" used to indicate that someone has developed a particular interest in something:
After I read "Shogun", I really got into Japan.
Here the speaker has not necessarily actually visited Japan, but has simply become unusually interested in some elements of Japanese culture.