We will be in Albuquerque and Santa Fe beginning of April. Any restaurant recommendations , preferably specializing in Southwest cooking?

Be sure to eat traditional New Mexican food (different from TexMex) which includes green-chile stews, blue corn dishes, purple pinto beans, Chile rellenos, blue-corn enchiladas and Sopapillas. Check out Mary & Tito’s in Alb. Sample Native American food at the Indian Pueblo Kitchen also in Alb.

Posters on Fodor’s recommend El Shed (New Mexican cuisine) in Santa Fe.

Tomasita's in Santa Fe, excellent drinks. Family feeling
La Plazuela at La Fonda. More refined, equally good food.

We tried to get into The Shed, but no luck.

Enjoy New Mexico

Santa Fe restaurant we liked a lot:
Cafe Pasqual’s
https://pasquals.com
We went for dinner and wished we had time to return another day.

Two places that came to mind have already been mentioned: Cafe Pasqual's and La Plazuela. For less refined, but still Southwest, check out Plaza Cafe Downtown, right on the square. Really tasty, we went back several times.

If you happen to be near Kakawa Chocolate, 15 min walk from square, definitely pop in for a memorable hot chocolate. They have a group of Mesoamerican chocolates mixed with various spices, including chili.
https://kakawachocolates.com/collect...colate-elixirs

We were last there in early March, 2020 just as the pandemic was unfolding, so I don't know what's changed. But it was interesting at the community table at Pasqual's, with everyone's hand sanitizer on hand. A good memory though.