Does reality exist when nobody is observing it?
No, at least not in the sense we normally mean by reality, a spacetime full of objects that would be there anyway. Subjective perspectives come first, and objective facts emerge from consensus between them. Each observer holds its own records, and a fact is a record that survives every comparison with the records of others. Spacetime is the meaning observers give to what they agree on, so with no observers at all there is no spacetime and nothing for a fact to be about. A universe with nothing holding a description is neither consistent nor inconsistent, and fails the test for existing at all. Nobody human has to be looking, though. An observer is any bounded system that keeps records and acts on them, and simple native observers at the base keep the physical world in place. Intelligent observers must evolve eventually, because only through them does the universe read itself into existence.
Also in Chapter 5: Why Do You and I See the Same Table?, Chapter 2: Why Is There Anything Rather Than Nothing?.
This answer comes from OPH, Observer Patch Holography. OPH is a rigorous, consistent and complete description of the unified, self-creating computational Universe we inhabit. Its consistency is machine-checked: the fixed point at its core is constructed explicitly, and a theory with a model contains no contradiction.
To understand OPH and check every step yourself, start with the free book Reverse Engineering Reality. It builds the theory from the ground up, and the OPH Notebook answers your questions while you read.
read the free bookask the notebookor ask sage:read chapter 3: Why Would a Universe Need Anybody In It?watch a universe make its own particles