If you don't need authorization, you can even host your app on one of the free services. For example, this single-web-page app hosted on jsBin.
Other platforms (Python, Java, etc.) should be just as amenable.
One caveat is that the Stack Exchange authentication methods currently don't seem to handle non-standard ports very well (there are some bug reports about this).
Also, for local development, you normally will want to set your app with:
- "Client Side Flow" enabled
- "Desktop OAuth Redirect Uri" enabled