I had some experience with this in when I doorknocked for the DFL in 2008, though it was GOTV so we were specifically targeting Democrats only and had houses marked on the plan to avoid that were Republicans. Not a lot of them of course, but they were there. This was in an semi-suburban part of NE Minneapolis granted.
Areas in Minneapolis that have a noticeable number of Republicans include:
-An area around a fundamentalist university (enough said).
-An area in a wealthy neighborhood near a country club.
-The U of M dorms. Yep, they're one of the most Republican parts of the state. Not surprising if you think about it though, as liberal as a school as that is, the dorms are going to have a strong population of rich College Republicans from the suburbs. The off-campus housing though is as Democratic as the city in general.
-NE Minneapolis, a semi-suburban area with a lot of ethnics. So kind of a less extreme version of the infamous NE Philly. Ward 1, the most northeast in the city, voted around 25% for McCain, that sounds pathetic, but having 1 in every 4 voter for him is a lot better to most areas of the city. Some of these are probably just your average middle class family Republicans, to some racist ethnics and law and order types, with some very religious thrown in the mix. I remember my doorknocking partner had a conversation with some younger woman who was "undecided" but did talk about wishing to vote for a candidate who best represented Christian values and the like. She clearly wasn't a Christian Coalition type, but if she voted Republican she's a good example of the type who are willing to vote Republican in the cities. Actually the Republican candidate in the State House district just south of me also fits, from her site she was basically a liberal on everything except abortion which she was militantly against (she was also a younger lady, around my age.)
The expensive downtown loft areas tend to be more Republican than my cheaper neighborhood, though both tend toward hipsters and the like, I suspect the downtown areas attract people who are stereotypically latte liberal but still vote Republican based on how much money they make. Please note these people are a big minority regardless, but they're clearly there. In the hyper-Democratic areas like where I live, it's probably poors who are just very religious or the type of religious voters I covered above, people who vote on it but aren't judgemental "BURN THE CITY OF SIN!" types who specifically avoid the city. There actually are people who think homosexuality is a sin yet don't believe in executing gays, don't freak out and hold prayer circles whenever gay marriage is legalized somewhere, and don't mind living in a city that gives recognition to unmarried couples living together who apply as "domestic partnerships", including homosexual couples (Two other cites in Minnesota do this too, St. Paul and Duluth.)
The DFL has some software that I've had access to at times which allows you to look up a score as to how partisan in either direction a registered voter is they use for phonebanking and the like based on their info an what they've learned. I looked up my apartment and was amused at how everyone was listed as Strong DFL or not assigned a score, no Republicans. My apartment could've voted 100% Obama, but remember that it only has about 25 people in it and is in an 89% Obama precinct. There's a tech school in the area, so they may have some of the McCain voters, a few straggling College Republicans. BTW I found sites for the GOP in all but one State Senate seat in Minneapolis (which happens to be my seat
), and while they aren't impressive in organization, (some are barely more than blogs), they're there.
Oh and if the 2008 caucus is any indication, a good chunk of Republicans were just your stereotypical Ron Paul nerds. Doubt they're still voting Republican though.