Nothing looks as established as the sites of the four Houses that this blog follows - the House of Commons; the House of Lords; the House of Representatives and the US Senate - though all have moved.Parliament once met wherever the King was, but over time Westminster became its exclusive site. The House of Lords was the first to have permanent accommodation. It met in the Painted Chamber for State Openings of Parliament and normally sat in the White Chamber. The House of Commons only gained its own chamber in the late 1540s - St Stephen's Chapel.
The Great Fire of 1834 destroyed most of the Palace of Westminster, and new chambers were built on the current sites. In 1941 a bomb destroyed the House of Commons and it met in the Chamber of the house of Lords until the current Commons chamber was opened in October 1950. In the meantime the Lords met in the Robing Room at the southern end of the Palace.
Congress has met in three cities. It's first home was Federal Hall in New York. From March 1789 until August 1790 the House of Representatives sat in a room on the first floor whilst the Senate met on the second floor (thus making it the 'upper house').
Philadelphia's County Courthouse, renamed Congress Hall, was the home during the 1790s. Again the House sat on the first floor and the Senate on the second floor.
When Congress moved to Washington in November 1800 on the North Wing of the building had been built. The House moved onto the 2nd floor of the west side while the senate took up residence on the 1st floor, on its eastern side. In 1801 a temporary wooden structure was put up on the foundations of the South wing. It looked like, and by all accounts, felt like an oven - which became its nickname.
The House returned to the North Wing in 1804 whilst a permanent South Wing was constructed. In March 1807 they moved into a chamber on the second floor. 
This lasted only until August 24th 1814 when the British burned down the Capitol Building. For the next few years Congress had to sit in a building which stood on the current site of the Supreme Court. It was often refered to as the 'Old Brick Capitol'. The House met on the second floor and the Senate on the 1st.
In 1820 the rebuilt Congress Building reopened. The House sat in what is now Statuary Hall. The Senate returned to its chamber (which was from 1861 - 1935 the supreme Court, previously the Court occupied a basement room below it). With the rapid expansion of the United States these chambers had become too small and two new wings were added in the decade before the Civil War. The House moved into its present chamber in December 1857, whilst the current Senate was occupied from January 1859 (though troops moved in during a recess in 1861 - when they left a few weeks later the chamber was described as filthy and "alive with lice."
