I've been in Santa Fe for 3 months for business and have eatten our a lot. Below are my favorites.
La Boca (1/2 off at Happy Hour from 3:00 to 5:00) - Get the Blood orange sangria
Favorite for New Mexican is Maria's and they take reservations.
I've spent the past few months in Santa Fe on business and I'm a solo diner most of the time and have found that most restaurants are accommodating, as well as vegetarian friendly, though below are some or my favorites for eating alone
Recommend: La Boca (my favorite restaurant in SF), Pasquals (community table), Outdoor patios are great - La Posada Hotel, Inn at Anasazi (patio or bar), Jambon (great food African / Caribean (bar and 2 community tables), Vinaigrette (salads), Shibumi (as someone already suggested (I sit at the equivalent of a sushi bar and watch the chefs cook. they are always nice to me when I dine there), The Tea House on Canyon Road
Good Luck and have fun dinning