Pop is pretty much capped at the number of +happy bonuses you have. Each city costs you 2 unhappiness before improvements, but a city that can work a new luxury gives you +5 happiness, for a net gain of +3 citizens to your cap, and thus to your science. Once you've got Construction, each Coliseum adds +4 happiness, for a net gain of +2 even for cities that don't work new luxuries. As you unlock more happiness buildings, the additional cities become more and more efficient.
There are also significant bonuses that scale with the number of cities. Maritime city-state food bonuses are significant, because they let you run Scientist specialists. The Citizenship Liberty bonus gives you +1 happiness per city, the Forbidden Palace is -1 unhappiness per city, and the Communism policy is -1 unhappiness per city - though honestly Communism comes late enough that it's not so important for research.
That said, not all city sites are equal. Scientist specialists have a very large effect on your science output, but require that you run a significant food surplus. You want tiles that yield 4+ food, and that typically means a river site for the +1 food / farm from Civil Service, or 3-4 Maritime allies. Once you got +6 food or so per city from city-states, even cities on relatively poor sites can be research powerhouses.