Short story about teleportation across the galaxy using alien teleport booths

Question

In this story, two male astronauts are on Mars and find a booth-like structure. One gets in and disappears. IIRC the second one follows him and is transported to a distant planet inhabited by intelligent, hostile reptiles. He gets back in and is transported again.

He visits and leaves a great variety of worlds, sometimes staying long, sometimes not; some have life, some don't. Eventually he realizes from the changing constellations that he is moving in a vast spiral across the Milky Way heading toward the core.

Answer 1

"Ticket to Anywhere" by Damon Knight, available at the Internet Archive. Near the end of the story the hero, Richard Falk, finds a message inscribed on a slab of rock by an earlier explorer:

THE DOORWAYS STOP THE AGING PROCESS. I WAS 32 WHEN I LEFT MARS, AM HARDLY OLDER NOW THOUGH I HAVE BEEN TRAVELING FROM STAR TO STAR FOR A TIME I BELIEVE CANNOT BE LESS THAN 20 YRS. BUT YOU MUST KEEP ON. I STOPPED HERE 2 YRS. FOUND MYSELF AGING—HAVE OBSERVED THAT MILKY WAY LOOKS NEARLY THE SAME FROM ALL PLANETS SO FAR VISITED. THAT CANNOT BE COINCIDENCE. BELIEVE THAT DOORWAY TRAVEL IS RANDOM ONLY WITHIN CONCENTRIC BELTS OF STARS & THAT SOONER OR LATER YOU HIT DOORWAY WHICH GIVES ENTRY TO NEXT INNERMOST BELT. IF I AM RIGHT, FINAL DESTINATION IS CENTER OF GALAXY. I HOPE TO SEE YOU THERE. — JAMES E. TANNER NATIVE OF EARTH