I am considering getting a cheap AppleTV 2 just to stream local music and video files but have not found a clear answer if Airplay will use my monthly ISP data allowance. Thanks
AirPlay is a peer to peer networking protocol, so it works even if you have no internet connection. In most cases, you don't even need WiFi for AirPlay to work so if you're really concerned, you could shut down WiFi or unplug it from the router entirely and check that things work.
AirPlay doesn't disable any background downloads or connections, so you could still use data while you AirPlay, but it's not because of AirPlay
Good discussion of AirPlay and LTE/Cellular data is on this thread, but your question is different in that it's more about WAN/LAN than a cellular link:
It does reinforce the "downloads can happen" aspect as well, but hopefully makes it clear the AirPlay is purely peer to peer and not routed traffic out a gateway be it WiFi or LTE.