When I got the game ( a couple months after it came out ) I installed it, and it was thrilling to be able to explore the west coast in a fallout game. But soon after, I realized that a clicking noise starts and becomes much louder than any other noise in the game. This happens every time I travel, in about 75% of the places in the game ( mostly in the southeast and northeast ) and even in buildings. It bothers me and even the people around me. Sometimes I have to quit the game to get the sound out of my head. I'm not sure why it's there, but I just want to know how to fix it, or how others with the same problem fixed it.

Assuming it's not the normal footstep sound, I'd make the guess it's a sound card issue. Driver, setting, soundcard software "feature" related, or maybe a sound encoder conflict perhaps. Maybe the footstep sounds aren't being rendered properly for some reason so you get a click instead of a thuddy footstep?

Anyway, if you want any chance of diagnosis, you need to post your PC info, like the dxdiag txt. file. A video with the sound wouldn't hurt either.

Realtek High definition audio version 6.00.0001.5791

What would you suggest I do if it were the footstep sound?

You could try turning down the footstep volume.
If that solves the issue then you should re-verify the files with steam.