There are currently almost 220,000 refugees registered with the UNHCR in Iraq, the majority in Iraqi Kurdistan. 
The majority of Syrian refugees in Iraq are in the Kurdistan province of Domiz (see map below).
In June 2014, the Islamic State of Iraq took control of the Iraqi city Mosul, sparking a second refugee crisis in the country. 

Iraqi Kurdistan

Refugee tents also at Arbat Transit Camp for Syrian Refugees in Sulaymaniyah, Iraqi Kurdistan, March 2014.
Dohuk
Domiz refugee camp
Moqebleh refugee camp
Erbil
Gawilan refugee camp
Kawergosk refugee camp
Basirma refugee camp
Qushtapa refugee camp
Darashakran refugee camp
​ Sulaymaniyah: Arbat transit camp

Most refugees from Syria in Iraq go here:

​More information: http://data.unhcr.org/syrianrefugees/country.php?id=103