I spend a few days cycling up and down Palawan and it's one of the better places i have cycled in the Philippines.
The roads are in a pretty good state and traffic is quite soft compared to most other places i have cycled in the Philippines.
You should still watch out for trucks and busses on the road as they can drive quite agressive at times, but in general it's a good place to cycle around as long as you can stand the heat.
The island has some mountains and you have some elevation there but you do not have any really long climbs, at least not in the parts of the island where i cycled.
You have resorts scatterd along the coastline, often a little out of the main towns and i always manged to find a place to stay the night along the road in various resorts and roadside hotels.
Favorite thing: I went to palawan. It was amazing. From flying on to a small airstrip to my last moments enjoying the views I felt very lucky to been there once. I stayed at El Nido which was something special. So many great places in the Philippines to have minute by minute adventures. Nov - Jan are the months that are the most comfortable as it does get hot. Its a great moment in my life.
Summer's from March to May. Nice time to enjoy the beach and get tanned. Plus the sea water is calm during these months.
If you are planning to go to Puerto Princesa and doesn't have a tight budget, you may consider Dos Palmas. If you're budget conscious, there are nice hotels in the city like Hotel Fleuriz and Legend Hotel.