There's an elevator on the far side of the Spanish Steps from the Hassler. Once it takes you to the base of the steps, you have a corridor to walk thru to exit. It's dirty and stinky, but seemed safe enough when I used it.

However, I will say that staying close to the Pantheon is my favorite location in Rome. It's an easy walk to the different fountains and squares of baroque Rome that I enjoy very much. I love sitting in one of the cafes outside the Pantheon, simply watching the world go by.