Inside the walls if you can — a handful of small lodgings put the wall-walk and castle at your doorstep. The new town across the bridge has the practical hostals and bar life. For silence, casas rurales in the hamlets up the valley are minutes away.
Buitrago del Lozoya lists around 10 bookable hotels and guesthouses, from roughly €44/night. Prices on the area page are live; booking 3–6 weeks out usually lands the best rate, with free cancellation on most rooms.
If it books out or you want to compare: Patones de Arriba (from €58/night), Rascafría (from €46/night), Manzanares el Real (from €48/night) — each with its own area guide on this site.
Curated picks are coming — meanwhile, the live search covers every bookable property at the same price or better.