Search through the Madridman boards, there is loads of info.

Barajas is a way out of the city so this is the reason you were finding it difficult to place them togther on a map. Try the Prado and Atocha, follow link:

http://callejero.lanetro.com/apps/lanetro/mapas/mapas.asp?id_via=2224&pais_geoc=ESPA%D1A&nombredevia=Calle+del+Gobernador&numerovia=0&nombre_fichero=ta1esp-madrd-madrid&lite_provin cia_geoc=Madrid&lite_municipio_geoc=Madrid

Metro it from airport to Madrid, cheapest and possibly quickest way to go.

Can't help with hotels in centre, but promise you that anywhere in the Sol, Atocha, Prado etc etc areas is walkable to the sights.

M.
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Where you see a crowd I see a flock.
It's sheep we're up against.

Everything you KNOW is wrong.