A bit exploity but:
If you have an aggressive AI personality for a neighbor who has strategic based UUs, look in their territory for that strategic. If they don't have it, sell yours to them as soon as you can (especially if you don't use it for your own UU). This can actually bait them into settling as usual instead of settling a city specifically to get the resource they want, and will often have them come back to you over and over for the trade?
The reason? If they do declare war on you, you cut the legs out from under those units. Rome attacking you and suddenly finding he's in iron deficit from declaring war, or Ghengis' war declaration suddenly leaving him with more Keshiks than he has horses to support can take the heat out of a few of the more aggressive guys.
Others:
-Remember that the Civil Service food bonus applies to all fresh water- not just rivers, but tiles bordering lakes and adjacent to oasis tiles as well (can take some of the pain out of desert-heavy starts). Fresh water also allows any bordering hills to be farmed as well; take that, Terrace Farms!
-Placing a diplomat in a city not only lets you negotiate for votes, but tells you the voting inclination of a civ in the first place. Check the WC after each diplomat settles in, it should update the Yea or Nay prediction count with your target's vote. In some cases, the guy you wanted to bribe could be planning to vote that way anyway, allowing you to save your money.
-CS negative influence caps at -60, and aside from Permanent War, won't overflow. If you want to be a jerk to them, do so all at once: bullying, attacking to take extra workers, and citadel bombing can actually all 3 be done to the same CS and often cleared (or forgotten within a few turns) by finishing a single quest for them.
-You will usually only get notifications on who built a wonder if you have an active embassy, diplomat, or spy in a civ's city. Other times, the notification will simply say it was built "in a far away land." However, if it's civ you've already met, their wonder list will be updated on the Global Politics screen, allowing you to always know who built it; presuming you've met them.
And finally:
-Some CS quests can give you strong hints if not outright data on your opponents. For example, if you see a quest for culture appear, hover over the quest icon on the first turn. If an AI is beating you, you can usually compare it to the cultural influence screen to know which AI, and you'll know their exact Culture per Turn. The same can be intuited by faith quests for determining the faith leader's exact Faith per Turn.