easy is to take metro line 8 at airport to Nuevos Ministerios and you are on the Castellana.
I usually do that and then they pick me up there. this is the line to the airport, and you can get off at colombia and link with line 9 or nuevos ministerios and take line 6 circular.
hotel we have plenty here go to Madrid hôtels all review by folks here, I stay with family or business hotel but hostal la plata in gran via is great near puerta del sol;listed here too
hope it helps