My short mental images are:
Lyran Commonwealth: Gleaming skyscrapers, bright lights, wide pavements. Big, impressive, symmetrical, clean lines, usually well-looked after. They are probably the ones who look the most like generic-sci-fi-future, so to speak. I could easily imagine a Lyran city
looking like this: advanced, busy, industrial, covered with lights.
Draconis Combine: Three-quarters of the city is a horrible, smog-filled
Blade-Runner-esque nightmare. Narrow roads, neon lights, people crammed into tiny square apartments with only a few basic amenities. The remaining quarter of the city is a luxurious noble district, aesthetically modelled on Tokugawa Japan with with modern technology seamlessly and silently integrated. (This impression may be entirely based on Luthien.)
Federated Suns: Cities are probably quite sprawling, since everyone likes a lot of space; I imagine lots of roads, car cultures, and heavy regionalisation. They don't go for giant metropoleis so much as lots of smaller cities networked together, and they like the countryside between them. Architecture features a lot of local flourishes, and faux-retro styles are often common. The 'high Davion' style is probably faux-medieval, with ornamental ramparts, spires, and gratuitous flags, but I don't think that's the rule everywhere.
Capellan Confederation: Not quite concrete blocks everywhere, but you can see the influence. Upscale districts are probably quite advanced, while poorer areas are less so - but they're all generally quite clean and don't have much urban decay, because the Confederation's strong ethic of public service. The Capellans seem like the sorts of people who'd taken broken windows theory to a high level. Recent constructions tend to deliberately evoke traditional Chinese architecture (or at least, what 31st century people think looks Chinese; I'm sure they wildly blend together different eras), and some older beings have been renovated appropriately. In wealthy areas it can be quite beautiful, but in poorer regions, the effect can be very chintzy.
Free Worlds League: My picture of the Free Worlds League is very Mediterranean, but that's probably only some regions. Diversity is probably the key here: not so much Davion-style local flair as what you get from a dozen different cultures of highly diverse origins, all of which rather dislike each other, living in close proximity for centuries. I imagine lots of architectural choices made to differentiate your district from that of the next people over; no one wants to be confused with them!
Clans: Concrete blocks. Decorations are for the weak.