Independence Hall served as the place where The Declaration of Independence for the United States was signed.
After the establishment of the Monroe Republic, the building came to serve as Sebastian Monroe's headquarters and main residence. This makes it a combination of the White House and the Capitol Building. Miles Matheson used it as his headquarters as well until he fled the Republic. Monroe began to hoard modern military equipment in the basement. It was also around this time that Rachel Matheson was imprisoned there. After Randall Flynn launched ICBM'S to Atlanta and Philadelphia both cities were destroyed, and it is quite likely that Independence Hall was destroyed as well.
The first floor of the building is largely the same as it was before the Blackout, with large open rooms for meetings and such. One of the rooms serves as Sebastian Monroe's main office, with several ornate pieces of furniture and a large desk. Monroe keeps several bottles of scotch on one table, along with his personal Desert Eagle sidearm. Tom Neville, Jason, Neville, John Faber, and others delivered important situation reports to him here. Another of these rooms served as a workspace for Rachel Matheson during her time there.
The second floor appears to be slightly altered, as storerooms have been turned into jail cells, and all available space is used for storing items, such as at least a dozen .50 calibre ammunition boxes. This is also apparently where Monroe has started to hoard modern military equipment.