I have multiple servers across the globe, running the same web application. The user is send to the closest server using DNS based 'load balancing' (Amazon's Route 53 with latency checks to be specific).
How do I go about checking the functionality of one of my servers? It would be nice to see a running application I can interact with and not just see if it is up or not.
Should I use a proxy near the specific instance or are there other options?
Depending on how exact you want the tests you can create a test plan then use Amazon Mechanical Turk to have users in different countries perform tests on your website. Its a small cost and probably the most exact test you can do. Proxies still aren't going to give you the best idea of how your applications performance will behave.
I came to the conclusion that using a proxy near the specific instance is definitely the way to go.
Hide My Ass offers a good list of public proxies. At the bottom of the page you'll find the instructions on how to use these proxies.