A very pleasant surprise
I didn't know about the State Capitol until I was on a walking tour (I highly recommend A Boot About Santa Fe) and was told there is an art collection here worth over $5 million. Just up the street from the San Miguel Mission you will find the Capitol. You can just walk in and enjoy the fantastic art collection on 3 floors; the business of the government is going on at the same time and you may run into officials going to a meeting while you are staring down from the top floor. There is no admission charge and no guards follow you around. Be sure to check out the grounds, the architecture of the building (no dome on this capitol) and the statues which surround it. Don't miss this treasure.