There is one place the Queen (or King) of England can not enter, What is this place and why can't she?

Her Majesty Queen Elizabeth II, not being a 'commoner', is not permitted to enter the House of Commons in the Houses of Parliament at Westminster.

Royalty is banned from the House of Commons, from 1642:

The gentleman usher of the black rod is the Queen's messenger, who has to summon the House of Commons into the royal presence in the House of Lords. Following the unpleasantness of 1642, when Charles I stormed into the Commons and tried to arrest five MPs, the lower house has made a great show of its independence. This takes the form of slamming the door of the chamber in the black rod's face, whereupon he raps on it three times with the eponymous ebony stick, and is allowed in to deliver the royal summons.

https://www.theguardian.com/world/2001/jun/20/qanda.derekbrown

see also
http://www.parl.gc.ca/HousePublications/Publication.aspx?DocId=2332189&Language=E&Mode=1
http://spartacus-educational.com/STUfivemembers.htm
The reason the Queen is not allowed into the House of Commons Chamber dates back to the time of King Charles I during the power struggle between the King and Parliament, which ended with Civil War and the King's execution. In January 1642 King Charles I and his armed men came to the House of Commons to arrest five of its Members for treason, but the wanted men had already fled. The Speaker, William Lenthall, politely gave up his chair for the King who demanded to know where they were. Kneeling at the King's feet the Speaker replied with words that have become famous in parliamentary history. 'May it please Your Majesty, I have neither eyes to see, nor tongue to speak in this place, but as the House is pleased to direct me, whose servant I am here, and I humbly beg Your Majesty's pardon that I cannot give any other answer than this to what Your Majesty is pleased to demand of me.' This reply left no doubt as to where the Speaker's first duty lay. The king had no choice but to leave and the role of the Speaker as the representative, or spokesperson, of the House of Commons was firmly established. Since that day no monarch has entered the House of Commons Chamber, which is why the State Opening of Parliament takes place in the House of Lords.

I should just add that the State Opening of Parliament (to which the House of Commons are summoned by Black Rod) does not take place in the House of Lords. It takes place in the Chamber of the House of Lords - i.e. the room in which the House of Lords sits). The Throne is not part of the House of Lords being the third part of Parliament (the Queen, House of Lords and House of Commons being the three) and her Throne and the area around it is not part of the House of Lords - hence why various people are allowed to sit on the steps around the Throne to listen to debates of the House of Lords as they are not techinically within the Chamber.