I lived in Albuquerque for a few years. The two most common things to do are to take the Sandia tram to the top and check out the hot air balloon scene. It was the longest tram in the world, but is now 2nd to one in like Bulgaria, or at least that's what I heard. I prefer driving around the backside and hiking to the top. You can also drive up there from the east side. Hiking the Sandias from the west side closer to Albuquerque is nice for a bit, although there isn't much for tree cover. It's much nicer around back. Balloon fiesta is amazing. Early in the morning you can see hot air balloons year round in the landscape.
Albuquerque is a very easy city to orient to. Get lost? Find the Sandias and that's due east. Everything is laid out in a grid.
I spent most of my time in Nob Hill which is a yuppie/hipster area. I used to spend a lot of time downtown on or near Central frequenting the bars for live music. Alas, I'm too old for that now being at the ripe age of 38, except for the Launchpad. Launchpad (minimal cover) and Burt's Tiki Lounge (free) are the places to catch music on the cheap. I've seen some amazing shows at the Launchpad which is a small venue that holds only about 150 people. I've seen Beirut, Calexico, the Album Leaf, Brett Dennon, and a whole lot more there.
Outside of ABQ, there are some cool Pueblos to check out. Acoma is really beautiful due west on I40. Up north, Taos is fun to check out for a day or 2. You can raft the Rio Grande gorge, the Box, which is always a good time. Around Los Alamos, there is Bandalier National Park with ancient native cliff dwellings. It's pretty cool and also good for kids. Northern New Mexico is really beautiful. There is plenty of info on Santa Fe. I've lived there too, and briefly in Taos. My parents are in Santa Fe.
Let me know if you need more info.