i myself come from Baguio, and i cannot think of anymore places to see aside from the typical (Mines View, John Hay, CBD, PMA)...
do the road trips from Baguio. Sagada is near Baguio, the mountain provinces (for ethnic taste) and Ilocos, La Union (for lowlands taste) depends on you though.
Asin Hotspring is in Benguet, if you have not visited it yet. the last time i went there took me less than an hour to reach the resorts but i suppose it will take less time now since the road is better.
Strawberry Farm is in Benguet (La Trinidad). From Benguet, you can move north, search the burial caves and try to climb Mt Pulag (next highest point from Mt Apo in Davao) through the amateur trail, it is colder than Baguio on top of the mountain.
You can also see the Ambuklao Dam, it is magnificent, but it will take around, 3-4more hours i think (the last time i went there).
You can also check out Balatoc Mines. They offer a tour in the mines and will be an educational trip.
Tam-Awan Village is a reconstructed native village which also has an art gallery and attracts many indigenous artists.