I have a language exchange buddy that tends to use this phrase a lot and from what I've heard it generally means 'something like that'. I've also heard that it's a phrase younger people use a lot to be indirect.
An example phrase would be:
.....と一緒に行ってみたいなぁ
How I would usually interpret this is "It would be nice to go with you"
If anyone could clarify the nuances of this phrase and its different uses I would very much appreciate that. Thank you!
～てみたい comes from ～てみる. It's simply the て form with the verb 見る (notice that it's usually written in かな alone, though).
～てみる means to "try to do something". For instance, 食べてみる (try to eat), 飲んでみる (try to drink), etc...
When you use the stem form of the verb + たい, it expresses the desire to do something. Some examples: 食べたい (I want to eat), 飲みたい (I want to drink), etc...
な is added at the end of sentences (like よ or ね) and has some different meanings. Check this answer for more details on that. In any case, it has a sense of confirmation in the case your asking. In English, it would be equivalent to the "isn't it?" at the of a sentence.
Summarising with your example, a more "literal" translation, with the underlying meaning between the parentheses, would be something like
I would like to try going with you (it would be nice don't you think?)
