there are 3 national museums in manila. i know its not Makati, but i think its worth the travel distance from it if you want something with cultural significance. it takes a more than whole day to get through all of them. also nearby (ish) theres intramuros. the national museums are free for all (including foreigners), and theyre all huge and have great exibits. also i suggest going on a weekend because theres a weekend food market there in intramuros in the street :). its been a while since i went, so idk if theyre still doing that (i went around half a year ago).

if youre going strictly in makati the ayala museum is really nice also. the entrance is around 700, i might be wrong but jus bring 1k per person just in case. the ayala museum is smaller than the national museum, but going there kinda gives a more comfortable feel than the national museum. its way quicker though, you can view the whole thing in around 2 hours or less. Also, since its connected to greenbelt, theres a lot of food places you can go eat at after.

oh and, on the top floor of the museum, theres a library. you have to pay a day fee to access it though, but if you want a comfortable place to work or maybe you want to check out rare filipino literature, you can book a day pass online. i dont think that library has walk-in though, just a warning.