I don't live in Santa Fe, but the wife and I got married there a few years ago, and went back to spend a few days there last November. I'm not going to pretend to know the place like a local, but here's some of the places we enjoyed:
La Boca, or its sister restaurant, Taberna La Boca. Great tapas place with a good mix of locals and visitors. It's right in the main square area.
Second Street Brewery - the Mrs. found this for a lunch/beer stop after hiking one day, and it was really good. Good beers, nice simple bar food, relaxed atmosphere.
Inn of the Loretto - we actually got married here on the terrace; their restaurant is excellent, and the bar/lounge area is really cool too.
If you guys are into outdoor activities, check out the hiking in the immediate area. Atalaya Trail is very close to the square, and while the top is steep, it's relatively easy if you're in decent shape, and has great views of the area.
If you're looking for a relatively inexpensive place to stay, check out The Old Santa Fe Inn. It's just off the square, and very nice.