If you have two or three days to explore the Great Wall, you will still probably want to avoid long travel times, so you will be visiting the wall in your vicinity.
There are different ways to explore the Great Wall for a few days. One way is to take a long walk from one place to another, sleeping on the wall or in nearby guest houses. Another way is to drive from place to place. Still another way is to remain in one well-chosen location.
If you're driving, you will select locations as described above under day trips. Guest houses aren't hard to find at all in these areas.
For a long walk, start to the west of Jiankou, at Wangquanyu, and hike east through Jiankou and Mutianyu to Lianhuachi and beyond. Or start at Lianhuachi and hike towards the west, through Mutianyu and Jiankou and beyond.
Many challenging long walks are also possible in Yanqing County, southwest of Badaling, all the way along the wall to its end at Bijiashan. This area is generally less populated and more isolated than the Great Wall in Huairou, probably because it is even more mountainous.
In a wall-rich location you can explore for several days. There are possibilities in all parts of the Great Wall where you could easily spend several days walking the wall in one area.