I used to travel with an ATA (long before OBi), but don't anymore -- the hassles have become worse, while the alternatives are now much better.
Don't depend on repurposing the room phone; hotels often have proprietary digital sets or IP phones. Worse, between infected machines, video-hungry guests, and the huge number of smartphones and tablets (carried by guests who would never bring their computer), many hotel systems are hopelessly overloaded and the connection is unsuitable for VoIP.
If you do have a solid Internet connection, you can call from your computer using Gmail or any softphone. Present Gmail behavior is that US/Canada calls are free (from a US-based GV account), even if you connect from a foreign IP address. For cordless, pair a Bluetooth headset to your PC's built-in Bluetooth, or to a USB Bluetooth dongle. Using a VoIP app on your smartphone or tablet, connect to hotel Wi-Fi. If it's weak or non-existent, use your laptop or travel router as a local hotspot.
When the hotel Internet sucks, the room phone may be a good choice. Many hotels offer free local calls -- you could use any calling card service. Or, call for free into your home OBi via a Localphone, Rebtel, iNum or SIPBroker gateway, then use the AA to call out on any of its services. If outbound is costly, a callback service (commercial or provided by your OBi) is often a good choice. Click-to-call is another option. This is easiest if your room has a dedicated DID. If not, but it can be reached through an IVR, use a PBXes account to dial the DTMF, or click-to-call from e.g. Anveo. If incoming calls must be routed through a human operator, try replacing the AA main menu prompt on your OBi with e.g. "Please connect me to John Doe in room 123". The OBi will say that three times before giving up, so you should have enough time to receive the call and press 2 to call out.
If neither of the above are suitable, there's always your cell phone. In many countries, you can get a cheap prepaid SIM; calling rates are outrageous, but incoming is free. This is a perfect match for callback from your OBi at home, or use a commercial service such as CallWithUs, Future-Nine or Fonworld. If traveling to several countries, consider Maxroam. Combined with a a US DID from them and OBi or GV callback, you get US inbound and outbound calling from much of the world for $0.12/min.
