When you use 在 with a time, where does 在 go in the sentence?
In the introductory Chinese courses I've seen they've taught two basic sentence structures:

STPVO and TSPVO


S = Subject
T = Time
P = Place
V = Verb
O = Object


Your sentence sounds quite strange to me, and I think it's because you're putting the place in front instead of the time or subject. Either of these variations sound much better:

我上个星期在日本看朋友。(STPVO)

上个星期我在日本看朋友。(TSPVO)

I don't think it's technically wrong to put 日本 first, but in that case you're putting much more emphasis on the place, which doesn't seem to be reflected in your English sentence.

In any case, you're right that 在 should go in front of 日本.