There is a common misconception embedded in the question "What is the capital of Baguio?"—Baguio is not a country or an administrative region with its own capital. It is a highly urbanized city located in the province of Benguet, in the northern part of Luzon island in the Philippines.
Known as the "Summer Capital of the Philippines" due to its cool, pine-scented mountain climate, Baguio serves as a major tourist, educational, and economic hub for the Cordillera region. However, the national capital of the Philippines is Manila (specifically, the City of Manila within Metro Manila).
So, while Baguio is a capital in a ceremonial, seasonal sense, Manila remains the seat of the national government.