5555555555 Sorry, couldn't help laughing at this one. You have to cover all the bases.
If I were to call the US from Thailand and I would neither want a charge to a US account nor a Thai number to show up on caller ID. I would use a prepaid calling card from my home country (i.e AT&T) and use their local Thai access number; this way there will be no caller ID or the ID will be from the home country. Another option is to install an Internet VoIP on the computer and call from the hotel room with High Speed Internet.