Dimmsdale City Hall is where The Mayor of Dimmsdale conducts city business. One time Vicky stormed into the mayor's office and blackmailed him into giving her power over the city. Another time she blackmailed him to vote for her in the Miss Dimmsdale Pageant or else everyone will see a picture of him in the 70's as blackmail (he tried to defend that those clothes were in style back then, but Vicky says to tell that to the voters which is enough to get him to help her).
This is where the mayor lives and this is also where a goat named Chompy lives too. The building highly resembles the White House in Washington D.C.