Fame
Much like salary, the fame part of being a local politician varies widely depending on the makeup, size, and circumstances of your place of residence. It's a pretty good bet that the people who voted for you know who you are, but sometimes they won't. You'll also find yourself on the front page of your local newspaper for all the good or bad things (mostly bad) you do for the community. But for the vast majority of mayors and city councilors, your fame will stay exactly where your power is: local.
There is, of course, the top level "local" politician: the big-city mayor. Those chief executives, especially those of the world-class metropolises, have the best chance of achieving national or even international name recognition. This shouldn't be a big surprise; if there's one thing America loves more than a good political fight, it's a good political fight that takes place on television.
America also loves its stories about ladder-climbing, so when we see a politician start as lowly mayor and rise to international superstar, it makes us feel all warm and gooey inside.
Fame isn't always what it's cracked up to be, though. There was even this one former mayor of a small town in Alaska who ended up becoming one of the most famous people around the world. Now, she spends most of her time shopping books and reality TV shows to the people who are still willing to take her phone calls.