We searched on GoDaddy and this is the result - "Sorry, google.city is not available." - it means google.city is booked.
Reading this thread made me want to buy the .city domain with my own city, unfortunately it was no longer available. But several other cities in my country are.
syda What city do you live in? are there any major cities available in your country? maybe pick the most populated one. I got a few big big cities. So if this domain goes big, I am going to hit it big.
I'm from Estonia, so there aren't too many big cities here. None actually I'm thinking of getting a few smaller ones, too bad I missed out on my own city.
Go to google search > click on advanced search > enter .city domain . So you can get a list of sites.