My answer for Manila usually depends on how traveled you and your group are. Manila can be a bit overwhelming to some if they haven't been abroad much. Intramuros is the best for a quick look at history and culture. But I haven't been inside the walls after dark, as mentioned above. The Mall of Asia and the Manila Bay area like Roxas Blvd. are pleasant for a nice walk to stretch out after long flights. Some of the newer better hotels are in these areas, or in Makati. If you want a bit more modern, or haven't been to SE Asia before and want the easy option, Makati or the Fort area have nice restaurants and are pretty clean and easy to navigate, also with some shopping options. In the Fort is the American Cemetery, which is fantastic IMO. I have been many times to there. But if you're not into the conflict history maybe not for you. (Although doesn't work for OP, if others browsing later have a full day, the tour to Corregidor is great also.)
And give yourself plenty of time getting to the airport the next morning. MNL can have some nasty traffic. Make sure the doorman at the hotel or whoever tells the cab driver where to go knows which terminal you're going to, as that adds a lot of time too going one terminal to the other.