Does it make sense to use KNN to target ticket buyers for arts events?
This is a classification problem that tries to answer the question: who is likely to buy a ticket to a particular type of show. If you have information about "the previous shows" that each patron attended, you can absolutely use KNN to find which patrons have similar aggregate viewership to a particular type of show. 

This might not work if you just have demographic information because there will be a lot of people that share the same demographics. However, as you mentioned, you can use the lat-long or zip code level information to get US census demographic data.

Evaluating the accuracy of this model is a little bit tricky, since you don't know who didn't attend a show due to external factors, but maybe you just want a quick and fast heuristic (which in my opinion sometimes works best).