Before you go: A number of nationalities can obtain a ten day tourist visa on arrival. If you are unable to obtain a visa on arrival, you will need to apply to an Iraqi embassy or consulate prior, and this may include obtaining a letter from the Iraqi Ministry of the Interior.
If flying, check with the airline on their understanding of your visa requirements. A certain airline (which I shall not name here) wrongly informed me that I required a letter from the Iraqi Ministry of the Interior and refused my boarding. That airline has since corrected their stance after I wrote a letter of complaint.
A visa on arrival will also state that you need to report to the Directorate of Residence within 15 days. However, it seems to only apply if you extend your stay beyond 15 days. I stayed for 10 days, never visited the Directorate and had no problems upon leaving.
Finding ATMs is problematic, so best to bring as much cash on you (especially US Dollars) to cover yourself for the entire trip.
Accommodation: There are some cheap options that offer poor value for money. I found it better to pay a bit more for a decent place. In Erbil, I stayed at the Kotri Salam (called the Peace Pigeon hotel in Lonely Planet), it was centrally located, with great staff and free Wifi. In Sulamaniyah, I headed to the Yadi hotel, which also had free breakfast and free Wifi. Whatever price you see advertised can be negotiated, so prepare to haggle.
Food: The Kurds are lavish in the meals they serve and eat. Great roast chickens can always be found, with falafel and a strong selection of Turkish meals also available. Eating is cheap but places can close early, so your options later at night may be limited. Western food (particularly pasta and pizza) are commonly found too, but is far more expensive than local options.
Transport: Taxi drivers are prone to overcharge foreigners so ask the price of the fare from your hotel, and use that information to gauge what is a fair fare. Between cities you can take either a bus or a more comfortable taxi, though the latter is more expensive. The prices on these routes seem to be the same for locals and foreigners. Road safety in Kurdistan is not strong, so don’t be afraid to tell a driver to slow down if their speed becomes ridiculous.