At MNL, stay airside—terminal transfers are slow and traffic is extreme, so eat and rest near your gate.
Stay airside. Road traffic between NAIA and Manila runs 45 to 90 minutes each way even outside rush hour, leaving almost no usable city time for a 3 to 6 hour layover after clearing immigration. The airport has multiple terminals, each with food and lounge options. Terminal 3 has the best retail and dining selection if you need to wait.
Head to Bonifacio Global City (BGC) in Taguig. Take Grab directly from NAIA Terminal 1, 2, or 3 to BGC High Street, which takes 20 to 35 minutes in normal traffic (PHP 300 to 500, around $5 to $9). BGC is walkable with good restaurants, coffee shops, and Bonifacio High Street open-air mall. Budget 90 minutes for the round-trip commute and 3 to 4 hours in BGC itself. Leave for the airport no later than 2.5 hours before your flight.
Add Intramuros to a BGC visit. The walled city is 20 to 30 minutes from NAIA by Grab (PHP 250 to 400). Walk the walls, visit Fort Santiago, and take a calesa (horse-drawn carriage) around the district. Budget 2 hours in Intramuros, then Grab to BGC for lunch or dinner before heading back to the airport.