For arguments sake, let's assume that travel and tourism is alive and well in Iraq. Iraq is really a country filled with a lot of history as well as culture. The best place to travel to right now is Kurdistan; they are the safest place in Iraq to be. They accept people from all over the world; they particularly like Westerners and the United States Dollar.
You will find most hotels in this area to be safe, but it may be hard to locate one of these hotels. Citizens of Kurdistan can recommend a good one and if you don't want to wait until you get there, you can place a call to your countries embassy and see if they can recommend any places to stay that are safe.
It may take you a few days to get to Iraq, it could take as much as 3 to 4 days. This will depend on the ground conditions as well as weather conditions. Once you are in Kurdistan you can travel to other parts of the country. But it is not recommended that you travel by car. With so many hazards on the road such as kidnappings and car jackings, the only way that it is recommended to travel is by armed escorts with cars.
There are some interesting cities in Iraq such as Baghdad, Mosul and Basra. These are the top three cities in Iraq with the most history and culture. There are old churches, monasteries and shrines all over Iraq. The oldest church in Iraq is located in Baghdad, it is known as the Church of Meskenta and the Church of the Virgin Mary is located in the Midan Square.
There are some hotels in Baghdad such as the Ishtar Sheraton Hotel, the Al-Mansour and the Palestine Meridien. These hotels are rated 5 star hotels but don't let that fool you. You have to remember that even as plush as the accommodations are you are still in a very dangerous city. Just because you are inside a hotel and not out on the street, you still have to be twice as careful.
Hopefully when all of the troops come home and the country gets deeper into the reconstruction there will be more opportunities to travel to what was once known as the Earth's first civilization. There really is some great history and some interesting sites to see.