I love to travel. I was a strategy consultant for several years, which is a traveling career based on business. While it allowed me to travel quite a lot, the travel wasn't relaxing or luxurious - it was mostly traveling to new cities for meetings in corporate offices. That said, I was still able to spend the evenings and the weekends exploring new cities. The compensation was quite good, and the work was intellectually stimulating. I'd recommend consulting as a job for recent college graduates who are interested in travel.
Caveat: Not every place you travel is going to be glamorous. I spent time in amazing cities like Paris, Tokyo, and Shanghai, but I also spent a lot of time in small towns in the midwest and industrial centers outside of Tokyo. You win some and you lose some.