Or think that grassland = desert. About a million acres of that “desert”, a lot of it right along I-40, burned last year. Who knew plain old desert would burn so well?
One of my favorite views in NM is off the back side of the summit of Sierra Blanca at Ski Apache. White Sands (and some real desert) is just below, while skiing in beautiful pine forrest on the front side. The Ruidoso/Cloudcroft area and the Hondo Valley are some more pretty funny looking desert.
Dag Otto, I agree about the views along I-40 east of Gallup. I think it’s a very scenic drive.
Duke of Rat, you’re right- Sierra Blanca/Ruidoso/Hondo Valley is a beautiful area. I haven’t been there in quite some time. I need to visit the southern part of the state more!
To get back to the OP, Lsura asked for lodging suggestions, so here are some motels in Albuquerque, at various I-40 exits, from east to west:
Tramway Blvd- Days Inn, Comfort Inn
Juan Tabo Blvd- Super 8
Eubank Blvd- Holiday Inn Express, Howard Johnson’s, Days Inn
San Mateo Blvd- La Quinta Inn, TraveLodge
Carlisle Blvd- Radisson, Econolodge
University Blvd- Hilton, Comfort Inn, Fairfield Inn, Super 8
There are more motels after you turn south on I-25, around the airport, but personally, I would choose anything on I-40 over anything down by the airport. I would not be afraid to stay at any of the motels I listed. It’s a good idea to remove anything of value from your car- don’t leave anything in plain sight that might attract thieves- but that’s true wherever you stay. It should be standard procedure when traveling.
Some good restaurants in Albuquerque are Sadie’s, Garduno’s, El Pinto, the Frontier- all of these serve excellent New Mexican food. If you prefer something else, I can make more suggestions!
I can also suggest some attractions that ARE close to the interstate in New Mexico- for example, Blue Hole in Santa Rosa on I-40. It’s a huge artesian spring, 80 ft. deep, with crystal clear water, popular with scuba divers.
In Albuquerque, there’s Old Town, Petroglyph National Monument, and the Tram.
On I-25, south of Socorro, is Bosque Del Apache National Wildlife Refuge.
On I-10, near Lordsburg, are some ghost towns, which I haven’t visited, so I can’t say if they are worth a stop.
Hope this helps, Lsura! Let me know if you want any more info!
Okay, I do apologize for referring to NM as bleak. It’s really not, and that’s an unfair judgment on my part. I was just having a “transplanted East Coaster” moment - being able to drive more than a few miles down a highway without hitting another town is still unsettling (I’m originally from New Jersey, so just blame it on the toxic waste I was raised around).
Bumbershoot mentioned the Frontier in Albuquerque - eat there! It’s this enormous, 24-hour place (that was curiously empty when I ate there last). It’s not fancy, but their food is awesome and it’s definitely got character. Wherever you eat, get green chili heaped on it. There’s a curious pathological New Mexican need to attempt to put it on pretty much everything, and good green chili is godly.
Hey, NinjaChick, I understand. As a transplanted New Mexican on the East Coast, I find the fact that it takes me an hour to go 30 miles bizarre, and the 55mph speed limits nearly offensive! 
Lsura, the answer is green chile ice cream. No, I’m not joking. Soooo tasty. The green chile cherry pie, I didn’t like so much. Though we’re pretty sure that was an accident…
My favorite New Mexican place, sadly, went the way of the dodo while I was in college. I’ve been gone from Albuquerque proper for eight years now, and NM as a whole for three, so I don’t feel like I have any major advice for you. I just hope you enjoy your trip!
I’m further east than you Lsura, about an hour south of Harrisburg, and I’ve done the drive to NM several times, never taking more than 2 days. Granted, those are 14-16 hour, 10 MPH over the speed limit days. 
I typically go as far as Arkansas or Missouri, depending on the route chosen and then crash for the night. One bit of caution-beware of NASCAR. I was returning from Albuquerque and had made it as far as Knoxville on day one when I elected to find a room. Everything was booked. After the third stop and being told the same thing, I learned that races were in Bristol, TN, and no rooms were to be had until I’d passed Roanoke. At that point, I napped in the comfort stop on I-81 for two hours and drove the rest of the way home.