score:4
You won't need a visa. You can check here: Applying for a Philippine Visa .
However, be careful with the timing. Manila traffic is terrible and it could take a long time to get to the city centre and back. Airport procedures can be slow. You will be able to make a token visit, enough to say: "I've been to Manila" but not much more than that.
If you want to do something specific, e.g. visit the palace, then research it carefully to ensure that it is feasible.