Sleeping on the Plaza Mayor itself — several small hotels occupy the balconied houses — is the whole point; book months ahead for weekends. The parador in the old convent is the luxurious alternative, one minute uphill. Weeknights the town is nearly private.
Chinchón lists around 14 bookable hotels and guesthouses, from roughly €55/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: Aranjuez (from €52/night), Alcalá de Henares (from €48/night), La Latina (from €40/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.