So in terms of "guild cities" (aka artist guild/writers guild/etc) you want to work those as much as possible, so I have those on most of the game. This is a good way to utilize food heavy cities (note that food heavy doesn't mean a lot of food tiles, it generally means a few really strong food tiles).
I always work the diplomat specialists when I first get them to get that first GD out. The first GD is very important because the extra paper really gives you some breathing room on having a few diplo units going around, before that paper is quite restricting. After that GD I generally keep those specialists until embassies run out on CS, and then I'll stop working them nearly as much.
Early in the game, its often a good idea to work 1-2 specialists when your city gets to 5 pop or so. At this point, happiness can be quite limiting and so you may not want your cities to grow fast, and so converting food into specialists is a lot more efficient than just turning off growth. If you have the library you get 1 specialist for no unhappiness so its easy to work an early scientist this way. Then you can turn the specialists off for a bit when happiness gets better to grow, and then regain the specialists once you have hit your happiness limits again.
Obviously if your unhappy (and would be even without specialists) than specialists become better. Your growth is already super nerfed at this point, so your not really losing any growth by working specialists.
A few other general tips:
- The Capital is generally my main specialist hub (doubly so for Tradition plays). The capital rarely has issues with local unhappiness and so can afford to work a bunch of specialists).
- Always maximize your GP production. Its much better to have 3 scientists in one city compared to 1 scientist in three cities as you will get your Great Person much quicker. So for example, while merchants are generally considered "underpowered", I may put two in a city as its specialists in order to get a Great merchant out, rather than sprinkle in a merchant here or there.
- Late game, you should generally be working as many scientists as you possibly can. There is no real equivalent to science at that point in the game, and specialists are the best way to get them.
- Beyond that, its a question of what tiles are available in your city. I wouldn't work a specialist over a resource tile, and certainly not a natural wonder. But over a "regular old tile".... yeah the yields of the specialist are normally pretty good.
- Growth wise, growth tends to slow down a lot after size 10 or so (non-capital). So yes you may want to lay off the specialists for some cities to grow it up....but once your at 10 or so I wouldn't worry about it too much. It takes long enough to grow, and the benefits of growth are weak enough....that generally I would rather milk the specialist yields.
