Some of my go-to mounting spots:
On the wall (at a height such that you can back up onto the dildo)
On a door (similar height as the wall, but like others have mentioned you can move the door back and forth for 'thrusting' instead of your body)
On the headboard of the bed (a wooden headboard, probably wouldn't work on fabric/leather/etc. kinds of headboards)
On dishware such as a metal sheet pan, the bottom of upside down flat-bottomed metal bowls (like water bowls) or cake tins, serving platters, etc. then you can ride it any place you want like on your bed (any dishware with large, smooth, flat surface that is sturdy enough and not breakable, avoid glass dishware for this purpose)
At the foot of the bedframe (if you have space between the bottom of the bedframe and the floor, you can get in 'doggystyle' position with your feet under the bedframe, on either side of the bedframe foot, and move back and forth on the dildo that way. Putting your feet on either side and backing up on the dildo also works if you have a wall that juts out, like for a closet door, where you can straddle the wall with your feet/legs on either side in standing or doggystyle position)

Whether each spot will work may depend on the paint/finish you have for these surfaces in your place (and not all dildo suction cups are created equal!)