The best way to see Santa Fe on a miser's budget (and yes I am a miser) is to fly into Albuquerque and book your stay there, and simply commute to Santa Fe by
RailRunner commuter train. Even a four star hotel can be found in Albuquerque for less than $120 per night (and well under if you shop carefully) while the same level of hotel will cost $230 per night and more in Santa Fe.
The RailRunner train is comfortable and fast and only $10 round-trip. Spend your money on good eats, and side trips to Taos and you will have a great vacation for much less money. Plus you will get to see three great cities (Albuquerque, Santa Fe, and Taos) for less than the cost of Santa Fe alone!