I am no expert on tuna but I have heard that there are restrictions on yellowfin and bluefin, while skipjack is ok - apparently, again its only hearsay and i haven't really checked up on it. not even the otherwise mandatory quick websearch. My wife and I went to Japan on our honeymoon more than 20 years ago and since then (and actually also before, which is why we chose japan) I have loved everything japanese. There is much more to japanese cuisine than sushi, but sushi is the most readily available outside japan.
In Denmark we have a sushi/yakitori crossover called sticks and sushi which is a very nice compromise if part of the family is not too fond of raw fish on rice. yakitori is grilled food and much more palatable for most kids than sushi, while still retaining the overall aesthetic which appeal to so many people.