最好这样说：因为听说台湾山的风景非常漂亮，所以我想跟他们一起去看看。

但是你的句子我觉得可以接受。

the construction VV看: 我觉得我不适合这份兼职，但是我还是想试试看。

逛逛看is kinda strange for me,I'm from northeastern China,and the only **看 phrase I can think of now is 走走看. And 逛 ,in my mind, is mostly used when you want to go shopping.

In northeastern dialect, we would use 溜达,转悠.

In standard Mandarin we would use 出去走走/转转

In your sentence,所以我想跟他们一起去看看 is good and idiomatic enough.