For your lodging, I highly recommend Guest Haven Baguio. It's ranked #1 among the B&Bs on TripAdvisor (perfect 5 stars), and has that classic Baguio cabin vibe. Unlike other hotels in Baguio, this place only has 4 rooms, and the service is very personal. The owners (a lovely couple) are the ones that actually greet you upon check-in, and the husband (who's a chef) personally cooks your breakfast (which tastes really good). Price is about P3k/night for a room for two, which is such a great bargain considering the service and quality of your accommodation.
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It's not a modern hotel, but you can find modern hotels everywhere. Instead, it offers you a rather unique and authentic Baguio experience.