I will assume you already have a relatively good understanding of the verb+の form as a nominaliser. It is similar to verb+こと.
Regarding ては, have you come across the verb+てはいけない structure before, meaning "do not do x"? This is probably the most common usage of the ては form, at least for beginners. It is essentially saying "if you do x, it will not do". In other words, ては is yet another conditional form.
From A Dictionary of Intermediate Japanese Grammar. p.463:
The conjunction TE WA is used to connect an action or state presented as a topic and a negative comment.
そんなに勉強しては、体をこわしますよ。 = If you study that hard you will ruin your health.
あの男は来ては邪魔になる。 = If he comes he will get in our way
So this is the theory behind it. I'm not sure about the example you gave though, I wonder if it should be 金曜日、日本へ行ってはどう思う？ And if that works, whether it has a negative or cynical nuance as per the above explanation from ADIJG.