Currently in the thick of both a civil war and a war with the United States (depending on your point of view) Iraq is not the vacation destination of choice for anyone without the support of a national military, major newspaper or international humanitarian organization behind them.
Businesses, journalists, and aid workers are also the only civilians to whom Iraq visas are being issued to right now, so even if you want to go, you may not be able to get into the country.
What to do
A trip to Iraq is a chance to get back to your roots. Iraq is home to some of the most ancient civilizations in the world and most of the empires have influenced the region either by conquering it or through trade. You can see the evidence of this rich history as a crossroads of cultures in the buildings and the people of Iraq.
You'll be limited by your visa status, but flights to Iraq have recently reopened with limited service. You can catch planes from Istanbul to Baghdad or London to Arbil, with periodic service from Jordan as well.
Where to stay
Iraqi hotels are generally not in the guidebooks, but they are available if you're in the country. It's not advised that you spend the night in these hotels or spend anytime in Iraq, but there are places to stay if you're there.