Hard to get the essence in 24 hrs, but some of my favorites:
Cliff House/Seal Rocks/Sutro Baths
Golden Gate Park
if you want to learn the history of the city – check out a big bus tour (i recommend the RED busses with the recorded tour guide for the most information – I’ve done both the RED and the Blue busses, and Red was worth the money). The tours will take you to every major attraction in the city, and you can hop on / off the bus for 24 hours.
Golden Gate Bridge (classic)
Mona Lisas (Best Italian Food in the city)
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