Ironically there was a thread in this forum a couple of years ago discussing bikes with similar features except they were being called "Country Bikes".
For whatever reason, I don't have too much trouble with categories likes "Downhill, Cross Country, Road Bike, Touring Bike, Cruiser, Cross Bike, and Utility Bike". For me, those terms describe fairly specific type of bikes though I'd agree that "Road Bike" is pretty generic.
I don't really like "City Bike", "Commuter Bike", or even "Hybrid". When I ride in the city, I see all of the above types of bikes, -especially while I'm commuting. It makes very little sense to me to have categories called "commuter" or "city bike". Part of what makes a city a city is that fact that it's not a homogeneous place. It's a collection of areas with very distinct flavors and sub-cultures. Likewise, there's not any single type of bike that people primarily use to ride in the city.
If I had to pick a type of bike to associate with the city, I'd pick a 70's or 80's road bike that's been converted to an SS or fixed gear or maybe tall bikes.