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.