Good to know about the car...that gives you a lot of flexibility. With the number of weeks you'll be in Abq, you should get a great taste of New Mexico.
Some ideas for your weekends:
Head up to Taos. Drive to Taos via the "low road" and return on the "high road" for the best views. Perhaps stay overnight if you can. Visit Taos Pueblo, a UNESCO World Heritage site. Have a green chile beer at Eske's Brew Pub. Visit the Rio Grande Gorge Bridge. Check out a museum or two. I recommend the Millicent Rogers Museum and the Harwood Museum of Art if you have interest. Drive the Enchanted Circle Scenic Byway. Hike to La Junta Point in the Wild Rivers Recration Area. Visit the Vietnam Veterans Memorial State Park. On the way back from Taos on the high road go through Chimayo, visit the Santuario de Chimayo and grab a meal at Rancho de Chimayo.
Between Albuquerque and Santa Fe, visit Kasha-Katuwe Tent Rocks National Monument.
North and then west of Santa Fe, check out Bandelier National Monument. I recommend not only the main section of the park in Frijoles Canyon (you get there by catching a shuttle from White Rock) but the disconnected Tsankawi section.
West of Albuquerque, you might want to check at the Sky City at Acoma Pueblo.
Plenty to do in Santa Fe with excellent museums, art galleries of all kinds, historic churches, shopping, great food, great beer. Some of my favorites:
Okay, plenty more possibilities to recommend, especially if we know more your interests...no reason you should be bored in New Mexico!