I think your friend was a bit unlucky.... Makati to the airport most times of the day is around 30 mins, in the middle of the night 20 mins to T3 and in early morning / late afternoon 45mins - 1 hour max. I've travelled to the airport from all over Manila many dozens of times and I can't remember taking 2 hours - ever. Plan for an hour to the airport wherever you say within the central districts and you should be fine - and always check in early in MNL - not an airport you need to be in a hurry in...
Where you stay depends where you want to go and what you want to see and do... Makati - crowded and clean(ish), Pasay - more crowded and dirty(very), Malate - kind of between the two. Pasay is a tad closer to the airport but that doesn't mean you want to stay there... Manila Metro is not very good - taxi's are cheap and walking is cheaper still. I'd stay in Malate or Makati, the former is handier for Metro stops and both have a wider range of hotels than Pasay with Malate being slightly cheaper for the same thing. Malate has plenty restaurants, bars, shopping etc. If you like Spanish Colonial, Intramuros is a 30 min walk from Malate across Luneta Park. Check out agoda.com for accomodation prices, to see what you get for your money (not as cheap as you think it should be) and tripadvisor.com is reasonable for reviews of what to see and do, restaurants etc.