ああ 水車小屋か
風情があっていいな
The character said this after stopping in front of a 水車小屋. Why is ていいな here being used here?
You appear to have parsed this incorrectly; it should be
[風情が][[あって]いい]な
the Verb/Adjective + て + いい construction meaning 'it is nice that it does/has/is...', or 'it is nice and ...'. Hence, here, 'it is nice and charming', 'it is nice that it has style' and so on.
Getting away from literal translation and structure, it's roughly equivalent to: "That water mill? It's got a certain charm. I like that."
It would be closer to: "That water mill? I like it's charm."
Put another way, the difference lies in whether 「いい」 applies to the water mill itself, or to its charm.