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Here are notes about a few places that were particularly special. Friends who've gone to some of these more recently tell me they've gotten very expensive. Current Madrid residents please advise...
Alkade - Jorge Juan, 10 - basque food - sopa de marisco, crema de centollo (crab soup), angulas (baby eels)
L'Hardy - Carrera de San Jeronima, 8 (Centro dist, Madrid); not typically Spanish, but excellent - beautiful main room - expensive (even then)
Restaurante Salvador - Barbieri, 12 - specializes in fish - fried and breaded hake (even if you don't think you want it fried and breaded, get it fried and breaded)
The tapa bars around the Plaza Major are fantastic.