In Civ 4 you would try to specialize a city.....food city....production city.....cottage city....is this still a viable strategy in Civ 5(should you only build one type of building and have tile improvements match the theme), or should you just build whatever is best for any particular individual tile?
I think so - I did it out of habit, and it seemed to work, anyway.
There are a few game mechanics in place that change up what we're used to. Health is gone, happiness is managed civ wide, granaries no longer manipulate the food bar, and Universal suffrage is available all game long. Net result is that you no longer invest (as many) hammers in infrastructure to achieve growth.
On the other hand, there's not going to be, I don't think, as much National Wonder focus as we are used to - the national wonders appear to require prerequisite buildings in every city, so unless you are investing a lot in infrastructure, you probably aren't going to build all the barracks everywhere so you can build Heroic Epic AND build universities everywhere so that you can build Oxford and ...
So consider a military pump: You've got Barracks, Armory, Military Academy for XP. You've also got buildings that give production bonuses depending on the build - Forge for land units, Stables for Mounted units, Harbors for naval units.
You probably wouldn't build a workshop, though, because that gives a bonus for buildings, not for units.
What tiles? Well, surely a balance of food and hammers in the early going, but you'll try to get more hammers when the City States start delivering pizzas
Like wise, your science center probably includes Library/University/Observatory/Public School/Research Lab. Workers can't build a science improvement, so you're probably looking at farms for specialists. but if you were to score a bunch of great scientists, you could put Academies on many tiles around the city, scoring multipliers instead of free techs. Somebody will need to do the math on this.
Gold is something real and concrete in this game, so it's easy to picture a city surrounded by trading posts, with the Market/Bank/Stock Exchange combo.
There are a bunch of buildings that only make sense if you have the right bonuses in the neighborhood, or that get some vigorish in that case - Monastery/Mint/...? so you may find that the local resources bias a city toward a particular specialization.
There are also more terrain specific buildings, so for games where you are planning a late era run, you may pay more attention to the possibilities of Longhouse/Solar Plant/Seaport/Hydroplant/Watermill/Windmill.
Happiness is global, so it wouldn't surprise me if some cities specialize on happiness buildings - drop a workshop in for the build bonus, then concentrate on Circus/Colosseum/Theater/Stadium. Hard to say - it may be that happy is better managed another way, or that cities eventually become responsible providing their own happy.
Because GP points are pooled separately, specialists slots aren't as key for GP farms, unless you are really planning to harvest different flavors of great person on purpose.