First of all, is city specialization dead?
OK, we still have production cities for units and wonders, and a huge capital where all kinds of booster buildings and national wonders are concentrated. But the rest seems to be random small cities.
I think it's very true that city specialization isn't as much of a 'thing' as it was in Civ 4. Certainly, you have placements that make more sense for hammer or gold cities, but since each city you place has such profound effects on your larger strategic situation, the consideration isn't simply the one niche your city is going to fill, it's how that city will change the strategic situation. That's a big change.
Regarding how to place them, that's almost an academic question. It's impossible to account for all the situations that happen on the ground, so really you have to develop something of a sense for both the city's resources (so you know what it'll look like in 10, 20, 30, 50, and 100 turns) and its place in your empire. It might be okay to go ahead and drop a city in a less than prime area if it will provide total control over a choke point, for example.
I'm not sure what you mean about 'not letting your cities grow large', though - unless you're operating under ICS, you want all your cities to be high population. There is no downside now to a large population now that
and
are gone, and every benefit now that science is directly tied to population. Unless playing ICS, I'm not sure I would even consider a city that didn't have food potential to support at least 10 citizens. Most temperate tiles produce 2 Food anyway, so you have plenty of space to plop down sawmills and trading posts (both of which I would consider more useful than farms in the general case, though there are exceptions).
The meat of it, I guess, is enumerating some of the criteria we use to decide on city placements. Really, you should look at the area 2 hexes around your potential city placement as the city's general 'zone', and the more of these points are within the initial 6 hexes, the better.
Good points:
+ At least 3 production squares (hills or forests)
+ 2+ river-adjacent tiles.
+ 2 or more bonus resources.
+ Access to any luxury (if you have a copy already, you can sell it for 300 gold to an AI).
+ Lots of 2 Food hexes (ideal trading post territory)
+ Access to strategic resources (Horses are especially good because they are common and the AIs will pay good gold for them into the industrial era)
+ Coastal (unless on Pangaea)
+ Choke point
Bad points:
- Abundance of unproductive hexes (desert, tundra, snow, etc)
- Marshlands (stunts growth)
- Too isolated from empire (don't drop cities in the middle of your rivals' territory)
- Requires 5+ road hexes to connect to trade network (don't pay more on upkeep than you'll get from the route)
- Bad visibility (when considering the rest of your empire)
Obviously, not all of these things matter all the time depending on what you need at the time, but it helps to have a small routine you run through your head.