1. Places to avoid: If you are visiting for vacation, go straight to the provinces, but exercise caution in the areas like Basilan, Sulu, Tawi-tawi, Maguindanao and Lanao del Sur because these places have a history of occasional disturbance. Other than those 5 areas, the other 75 provinces of the Philippines are just fine. Metro Manila is safe to visit but there is currently a daily challenge we all have to face here — traffic. Metro Manila is so congested with traffic that you will mostly spend your daytime in a vehicle. I'm not dissuading you to visit Metro Manila but just set your expectations that mobility is not easy here.
2. Airport arrivals: If you can select your arrival airport, avoid NAIA. Instead, pick a flight that lands in Clark (CRK) if you are traveling to Luzon area, or Cebu (CEB) if you are travelling to the Visayas, or Davao (DVO) if traveling to Mindanao areas.
3. Transportation from the airport — avoid people who offer you ride because they will charge you exorbitant rates, instead, look for the taxi/cabs being monitored by the local airport police, they have their own queue at the airport, or you may opt to book via a ride hailing service like Grab, or you may opt to ride a point-to-point bus service if your destination is along their route. Another option is to arrange for airport pick-up service through your hotel before your arrival.
4. Local transportation: If you still want to commute within Metro Manila, I would recommend the trains — MRT, LRT1, LRT2 and PNR (although some of the trains are not air-conditioned). Compared to industrialized nations, trains in Metro Manila are still few with just 4 lines at the moment (with 5 upcoming lines). These lines can be crowded during rush hour but outside of that, they’re convenient. I personally take these to my business meetings (leaving the car at home). For places not along those lines, take a ride hailing service like Grab, it is more convenient than regular taxis. If taxis are your only option, avoid getting one from the streets. Instead, book them by calling their dispatcher (you can get these from your hotel).
5. Driving: Even if you can drive, do not even try it especially in Metro Manila because it is not a pleasant way to spend your day due to traffic. Outside of the larger cities, you may drive at your leisure and avoid breaking traffic rules even if you see locals do it.
6. Pedestrian lanes: If you walk on the streets, avoid thinking that a zebra/pedestrian lane is safe place to cross - drivers ignore it because it is not enforced by the police here, always look first before crossing. Pedestrian lanes with stop lights are generally respected.
7. Just like any other country, avoid doing anything illegal and you will be just fine.

Finally, besides what was mentioned in #1, there is more to appreciate in other places in the Philippines so do spend time to relax in one of our islands because we have more to offer than what you see in the news. We have 7,641 islands, here is one: