Upper back: Superman lat pulls
If you have access to a pull-up bar, pull-ups are always going to be your best bet for a bodyweight exercise that targets your upper back. And yet, a pull-up bar is technically equipment, so I'm not going to assume you have access to one. Which actually makes it really hard to find solid exercises that target the large muscle groups of the upper back. Hard, but not impossible.
The Superman lat pulls exercise is typically performed with a resistance band to provide extra resistance, but even without a band it's a challenging exercise because you're forced to work against gravity as you perform the movements.
Lie on your stomach on a mat, your arms extended in front of you, your legs fully extended behind you. Tighten your core and use your abs, low back, and glutes to lift your chest, shoulders, and arms off the ground. From this position, tighten the muscles of your shoulders and upper back and squeeze your shoulder blades together as you bend your elbows outward, drawing your hands toward your shoulders. The trick is to really focus on squeezing your shoulder blades together.
When your hands are just in front of your shoulders, reverse the movement, extending your arms in front of you. Further engage your upper back and shoulders by consciously working against gravity as you aim to keep your hands in a single plane -- don't allow them to drop closer to the floor. Perform 15 to 25 repetitions.