Accumilating buildings

I'm a long term Civ Player and still cannot work out some good accumilating building

For example

Library
Great Library
School
University

All give bonus to research,

Production example

Workshop
Forge


now my question is

What would be the best progess for research bonuses per city

I've seen some ppl who masterminds the research efficiency. Not as a civ combined.

1 city, if worked right can easily earn 100-300 tech points per turn, even before the industrial age.
Can anybody throw me a bone and give a few pointers for specialising the cities. I understand city placing and what tiles are best for each city. The question is really about buildings que.

Research
Production
Culture
Turism
Gold
& a
Supercity - City Growth

You're in the right direction. But you're forgetting about the new trade routes. It really helps after you build a Granary to send food over to your capital/2nd city. Your growth will sky rocket - resulting in more citizens and thus more science.