Kelly's right, travel photography is very difficult to break into. Costs are high, clients are few, and it's something that everyone wants to do. It's also very difficult to get a magazine to trust you with your first travel assignment, because if it doesn't work out, they're out a lot of money.
One thing worth noting though - doing travel photography is not like traveling for a vacation. A lot of people don't realize this (I'm generalizing, not saying anyone here on this thread) It's work, hard work, and I've seen photographers fail because they get caught up in enjoying themselves in a vacation way and forgetting about the job they came to do. That being said...
I have two thoughts for getting started. One is the travel section of your local newspaper. You could pitch story ideas to them of semi-local stuff (day trip type things). It might even be best if you take photos before you pitch the story. Shooting places you're familar with in a new and different way is always a challenge.
I know a photo editor who's been in the business for 30+ years that always asks photogs he wants to work with to see their local stuff. You tend to stop seeing the stuff you see every day and if you can push your creativity to see it in a new and exciting way, that extra bit of determination and creative energy, that's key (in my mind).
My second thought was travel stock photography. There's a great site
www.alamy.com where you can post photos you've taken as available for sale. They take a % of each sale (read the terms & conditions carefully and decide for yourself if it's worthwhile to you). But if you can build a strong portfolio of travel iimages (again, could be based on local stuff) and make some money selling stock along the way, you'd be better off than a lot of folks. Plus if your stock images sell, you normally get a photo credit, which definitely legitimizes you in the eyes of photo buyers (again, my opinion).
But please, stay away from micropayment stock sites like
www.istockphoto.com - you'd be really selling yourself short. They pay less than $1 to the photographer when a picture is licensed. With a site like Alamy, you could be making $50+ (which is still cheap) each time an image is licensed. Of course, you need stronger quality to get images placed with Alamy, but it's well worth it IMHO.
Hope that's helpful in some way. If you have any other questions, I'd be glad to try and answer them.
BTW - Classes are a great way to learn, no doubt (says someone w/ a bachelor's degree in photography) but get out there and shoot - experiment, play. You won't hit a home run all the time, but you'll learn a lot.