The victory overview provides some information to how close each civ is to a victory condition. The demographics screen gives numbers which indicate which civ is doing the best/worst in certain categories.
You can see each civ's tourism compared to other civ's culture in the culture overview. You can determine each civ's technological progress by hovering over their score. Divide that by 4 to get their # of technologies (including agriculture). You can determine the number of city state allies a civ has by going to the world congress screen or just counting which city state is allied to which civ.