Inexpensive short dulcimer
Instruments- discuss specific features, luthiers, instrument problems & questions
Lisa, the danger buying most of the cheap dulcimers out there is that they are not really instruments but "dulcimer-shaped objects" intended to be hung on a wall somewhere rather than played. A lot of them have really high action, making them hard to play, and many don't even have correct intonation, so you will sound off even if you are playing correctly.
Bill Berg and David Lynch are two reputable luthiers who make "student" dulcimers for less than $150. They are real instruments and will encourage you to play. However, they are not really small travel dulcimers. The small dulcimers don't really cost less than the big ones since they involve basically the same amount of work. One option for you might be a cardboard dulcimer. Folkcraft sells some that you can either put together yourself or buy pre-assembled. I played one at a festival a couple of years ago and was amazed how well it sounded, although obviously it did not have extraordinary volume.
But I should also say that I own several really nice small dulcimers, including octave dulcimers by Ron Ewing and David Beede. They are small enough to fit in a decent-sized backpack or under the seat in front of you on a plane and yet they both have a really charming tone. They don't have a lot of sustain, but they stand out in a group of dulcimers because of the higher pitch. They are not really cheap, but they are delightful instruments that maintain their value pretty well.