Dampa/Filo restaurant recommendations /day trips (Manila)

Hi all,

I have a friend here for 3 days and he wants to experience true Filipino culture. I've arranged a Carlos Celdran tour as well as a few museums to check out.
Wondering where the best 'dampa' is or if you can recommend any good Filipino restaurants with a good vibe that feels and tastes authentic. I've been to many around the Fort and Makati which haven't really satisfied the tastebuds.
Also, any quick getaways to scenic look outs in Manila that you can recommend given that it's a short trip to Manila?

Cheers!