As far as I know no single city has done such a study, partially because carry is generally tracked at the state level. However:
http://www.seattlepi.com/local/377385_gunpermits02.html
that gives at least one or two county permit numbers. The numbers have continued increasing in Washington. Right now carry is at about 7-8% of eligible persons. We're among the highest in the nation. While it's true that not every place in Washington is a city, the VAST majority of the population (85%) lives in one.
Hrm, google search shows 6.6M population in Washington, so 3.8% carry rate. So maybe 1 in 50 people you run into has a gun, depending on how often people with the license carry. This is a rate I'm not terribly concerned about. If law abiding citizens who are willing to go through enough hoops want to carry guns it doesn't really concern me I think any claims of increased violence are just as statistically irrelevant as claims of decreased crime.
I simply don't believe our forefathers had a perception of modern society when they envisioned the entire populace armed. In the late 1700's most of the country probably didn't see much more than their family for an entire day or two. In a society where you potentially cross the paths of thousands of individuals each with their own quarks and flaws which are part of human nature I don't think significant carry rates are practical.