I learned to play an acoustic strummy version of Hotel California, with no capo with the following chords: verse Bm – F#7 – A – E – G – D - Em – F#7 (btw, how many songs start out with 7 different chords?!) and chorus: G – D – F#7 – Bm – G – D – Em – F#7. These particular chords allow for some nice embellishments which bring out some of the melody.
Out of curiosity, I watched a live performance by the Eagles and there were three and a half guitars: Don Felder plays a double-necked Gibson 
. He plays the intro on the 12-string neck capoed at 7 and later he also plays some fills on the 12-string, but mostly during the rest of the song, he seems to play fills on the 6-string neck.
Joe Walsh plays a Tele (no capo) and plays those classic fills you hear during the chorus, plus strums the chords during the verses.
Glen Frey plays a 12-string acoustic capoed at 2, strumming the chords given by @Jwaters above.
The iconic “solo” is played by both Felder (6-string) and Walsh. At first they take turns, later on they play together.
Eagles - Hotel California (Live 1977) (Official Video) [HD] - YouTube
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