Culture: Sistine Chapel
Commerce: Machu Pichu if wide/warmongering, colossus if tall
Happiness: Notre Dame
Religion: Hagia Sofia (if need 2nd prophet), Mosque of Jenne otherwise
Science: Porcelain Tower
Military: Alhambra
Best overall: Temple of Artemis
Sistine: +25% empire-wide is a lot even on a 4-city game. On a wide game? Incredible for both rapid border expansion and policy acquisition. Hits everything blanket-wise including religious buildings, guild slots, etc. a lot of compound interest.
Machu Pichu: can't often get it, but when I do it is a lot of extra gold. Colossus probably better on a tall game due to extra route early + gold on routes to you, but in a wide game Machu can easily reach +50 gold flat for your city connections or more. I like it in concert with my conquest games as the gold doesn't require trading with others which colossus does. It is my savior when everyone stops trading with me for gold income.
Notre Dame: I've heard arguments for FP, but I just can seem to make that -10% pass 10 happiness total. I need 200 population for it too and I never get this until pretty late-game. A flat 10 at that time period is just perfect for alleviating happiness and growth problems.
Hagia Sofia: Free temple (usually 2 gpt) and +3 faith plus prophet for instant enhancing. Hagia is the savior to an empire struggling in faith gen for a quick enhancement. In some games I'm already enhanced and this is less valuable to me compared to Mosque of Jenne. Mosque is far more valuable on games where I need to evangelize aggressively (huge game, tithes, 3 nearby AI with no religion to speak of). Having Mosque makes tithes ramp up so quick and my faith spread like crazy. A few games I've manage Mosque + Borobadur back-to-back for 3, 3-use instant missionaries, a free mosque, and +8 faith base. I was unstoppable and faith everywhere a few turns later, as I'd do the trick where I focused on tiny cities and skipped middle ones letting the pressure fill in. Managed to convert almost entire continent with just the 3 in about 50 turns. Usually a great game afterwards. Couples amazingly with evangelism if you are role-playing and intend to forcibly convert most of the world as well. They're basically unstoppable 3-use mini-prophets that add +6 followers and subtract as much from the other faith per use.
Porcelain Tower: Free GS, +2 GS points, +50% to all RA's the science bonuses on this thing easily shave of 30 turns from your finish time in my experience.
Alhambra: Brandenburg is good and all but super-late. This thing doesn't just give some xp though, it gives a free upgrade on top of barracks+military academy. Results in 3 starter upgrades, plus a free castle for perks, and oh, +20% to your culture randomly. If it wasn't good enough already having the +20% to culture cinches it--like a second sistine for that city.
Temple of Artemis: Leaning Tower is amazing really, quite good, but ToA? Even better, mainly in my opinion bc if you can get it you get in the the first 50 turns of the game so the rest of the game you have a pre-eat + 10% to all your food empire-wide. Easily the best food buff there is. Pre-eat means you get compound interest on it and as your food base grows it is a direct multiplier so you grow faster and faster. In my experience if you can keep the happiness to use it, ToA easily grows you far more than 10% as fast, maybe more like 20-25% effectively, and the effect becomes stronger over time alleviating long grow times late game. It's useful all game long and only becomes more powerful.
