@PublicWolf off the top of my head I suggest going on a tour with renacimiento manila. they post scheds ahead of time.
🔗 https://www.instagram.com/rebirth.manila?igsh=MTl1ZHgybHFydm11cw==
places I usually take visitors besides the intramuros area and the national museums:
quezon city: cubao expo, gyud food hub/ mang larry's, vargas museum (up diliman campus)
makati city: ayala museum, little tokyo
san juan city: corner house, pinaglabanan park (museo el deposito), greenhills mall
p.s: as a local, I just use grab. much safer.