Prince/Small is kinda close to the games I'd normally play. Couple disclaimers before I answer: One, I play strictly for fun, rarely try to challenge myself, in fact I hardly ever even finish a game. So I don't normally have "Space race" or "Culture" or "Dom/Conquest" in my head from the begininning of the game. Two, I'm hardly an expert. Having said that...
Burcap. If the RNG gods gave you good cottage land in your capital's fat cross, grow the city as quick as you can and start growing the cottages. Pop a GSci as soon as you're able and use him for an Academy. With a somewhat larger empire I'd probably look for a more pure commerce city to put Oxford in later, but if I'm playing a Small map I'm only looking to have 4-6 cities (plus whatever colonies/conquests later on). So, since I might not get a good spot for a cottage city, I'll plan on building Oxford in the capital. (Along with all the science-boosting buildings.)
GP farm. Probably the most important city to specialize. Find a spot with a ton of food (food resources with riverside/lakeside grassland to farm), preferably with at least some production for specialist buildings and maybe Wonders. Personal preference- I'm a lot happier if my GP farm's BFC doesn't have any commerce resources in it (gems, dye, etc.) That part also applies to...
Unit pump. Lots of hills to mine, hopefully some production resources, enough food to work the production tiles. Build HE here when you can, usually I'd pair it with WP or IW later on.
If there's a spot with decent food, good commerce, and at least a little production, that's where I'll put my money city. It'll get Wall Street and whatever corporate HQs I start. A shrine is nice, but founding early religions is generally not the best idea, and it's hard to justify wasting beakers on Divine Right just to have the RNG drop Islam's holy city in my unit pump.
Most games I try to get a "secondary" GP farm-type city up and running and use it to run spy specialists, but if my entire empire is only 4 or 5 cities that probably wouldn't happen.
Edits and addendums...
Mostly, all that had to do with core cities, because a Small map will probably fill up pretty fast. (Well, I usually play with an extra AI or two anyway, that has a lot to do with it.)
As far as Wonders, that usually doesn't factor in very much for me, but there's a few things I think about. If there's a wonder I've decided to build, I'll put it in my GP farm if I can- unless the GPP goes to a GArtist in which case I might look elsewhere. However, unless my GP farm has more production than normal, most of the time it's building specialist buildings and can't waste the hammers on wonders. If I can, I'll build the GreatLib there.
This rarely works out this way (except maybe Industrious leader games), but
if I'm building Pyramids
and Hanging Gardens (and possibly Hagia later), I'll try to build them all in the same city for the GEng points.