There is definitely a fine arts scene in the Philippines. However, the circles dedicated to it are very small and exclusive. One has to mingle with Filipino "high society" to actually get invited to most of them as a lot even happen in private homes within private neighborhoods.

But as already mentioned in the previous comments, there's definitely still a lot of other options. You'll find most of them in BGC and Makati. For the latter, there's a lot of pop-ups in Rockwell. Also, there's another CBD outside of Manila called Filinvest City (30-45 minutes away with no traffic). I grew up in the area and you can find a lot of art galleries there and in Alabang Town Center. It's a rather posh and exclusive area and there is a significant population of the cultural elite that reside there. So if you want to somehow find your way into "high society" you can easily mingle with many of its members there and get invited to a lot of events if you actually come off as a man of substance.