Mercedes,
There really are some beautiful places between Albuquerque and Denver and not too far off the interstate. If you like wide open country and prairie stay in northern New Mexico. I like Sugarite State Park. This meets your elevation requirements. There aren’t any major trails but you can put some smaller ones together for a good hike and it is an “underused” park so a good chance that there won’t be many people. I don’t remember the camping site requirements.
If you can spare the time to drive there, there are some great trails near Westcliffe, CO on the eastside of the Sangre De Cristos and the westside of the Wet Mountains. Just do a search of hiking trails near there. Beautiful mountains! Beautiful valley! But the topography can get up there and quickly.
And then almost right along the interstate are the Wet Mountains just to the west of Rye and Colorado City. There are some good trails there and hardly any people. You can also do a search of those mountains and their highest peak, Greenhorn Mountain, to locate trails and maps.
I hope you can find something that will work for you.