Plaza de Santa Ana and Calle del Prado are the classic addresses — lively until midnight, elegant after. Downhill toward Antón Martín the barrio gets more local and cheaper, with the Mercado de Antón Martín's stalls as your canteen. Anything here is under 10 minutes' walk from all three museums of the Golden Triangle.
Huertas — Barrio de las Letras lists around 260 bookable hotels and guesthouses, from roughly €47/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: Sol (from €45/night), Lavapiés (from €35/night), Gran Vía (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.