To add my perspective, "city" means urban Seattle. I live right in the geographic center of the city, and in my neighborhood a lot of roads I contend with are very narrow, with lots of intersections, parked cars lining the road, etc.
You can get anywhere in Seattle proper without breaking 40mph, if you're patient, but being capable of 55-60 makes things easier. Mostly, acceleration from a stop and power for hills (we have many, and they are steep) are key.
Lane splitting/filtering is not legal here, but being small does have advantages for being able to sneak around cars waiting to turn, which itself is enough of an advantage to make my car feel like a burden. A tight turning radius is also a great benefit, as it lets you take advantage of these gaps in stop-and-go traffic as they open.
I think a good 125-150cc is perfect here. My mostly-stock Stella gets me away from normal traffic at lights and keeps up on all the hills, while being small and nimble for making quick u-turns and sneaking past cars. My old Vino 125 did well, too.
Overwhelmingly, the scooterists I know are also on 125-150cc or similar-framed bikes (i.e. a P200). The most common modern 200-300cc bikes are the modern Vespas, which are much smaller, nimbler, and lighter than your standard 250cc maxi.