Hi khatrineluz, you can choose from the many budget hotels in Baguio including Rajah Soliman hotel, Belfranlt hotel and Villa La Maja hotel. I have stayed once at Belfranlt hotel which is located in General Luna road, Bagiou. It offered good services and easy access to nearby attractions.
Philippines is filled with wordwide travelers from March to June, so during January many of the hotels in Baguio will not be crowded and January is a perfect month for budget-conscious travelers. Even airfares from
Manila to Bagiou will be cheaper, so ask them to book in advance for a nice journey.