Find your level and work your way beyond it, using those newspaper travel clips to convince editors at magazines that you can handle assignments on contract. If you enjoy wasting time and stamps, go ahead, send your work to the New Yorker or Atlantic Monthly. In the long run, you'll earn a steadier part-time income and advance your career faster if you focus on regional, trade and special interest magazines. Find those magazines on newsstands, on the internet, on a friend's coffee table. Almost all special interest magazines are hungry for stories with a travel focus that addresses the magazine's stated purpose, e.g. antiques, chocolate, glass collecting, railroading, whatever.
Regional magazines are another break-in travel market.
Many states, cities, recreational regions put out magazines aimed to attract tourists or promote local business. Sometimes the state economic and development commission has a hand in producing those magazines. Local writers have an edge. Remember that regional travel magazines come and go rapidly. Evaluate the magazine's finances carefully before sending a query or working on a story.