The safest bigger city to visit in Iraq is probably Erbil, and this city in the Kurdistan Region of Iraq has a moderately big expat population. Any city in the Kurdistan region is one of the safer ones in Iraq.
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Iraq - Level 4: Do Not Travel. Reissued with obsolete COVID-19 page links removed. Do not travel to Iraq due to terrorism, kidnapping, armed conflict, civil unrest, and Mission Iraq's limited capacity to provide support to U.S. citizens.
The capital has lived some pretty dark days in its recent past, but it's also one of the places which has seen the biggest security improvement. Nowadays, I personally believe that Baghdad is a safe city to travel to. There's a lot of security, you can walk around freely, and the locals are very nice.
A Passport (valid for at least six months) and visa are required for most private American citizens who plan to visit Iraq. Travelers should not rely on obtaining a visa upon arrival at an airport or port of entry in Iraq.