I travel with two watches. The first is a radio-controlled Seiko SPBG003 digital with world time, dual time, timer, chronograph, alarm for flights and casual use. I also have a Bulova Gemini 63B014 GMT automatic for business or dressier occasions when the digital wouldn't be appropriate. Both watches are now out of production but I've got less than $600 in both of them so don't mind if they get lost along the way.
The nicer watches stay at home.