In reply to Valkyrie1968:
I look for novelty and at least one nice move.
It's easier to explain with indoor bouldering, but the idea works for less and even top ropes I think.
Novelty. I want a climb that makes me think. I want something to involve more than just strength. The route may meander across the wall or may have an element of moving back down before reaching the top. Volumes or features may either help or hinder, or both.
If the route can teach me something eg balance or technique, then I learn something, which feels good. At the top of my admittedly low grade, I like to think of it as a friendly, quiet, almost personal competition between me and the setter. Sometimes I win, sometimes they win. They make me move my body in a certain way, or I find a shortcut, or I fail. A route without the headology is boring.
One nice move. This may be the test piece from the lesson. It may be something that just feels good. Personally I like moves requiring a change of balance from one good position to another via a heart in the mouth swing or unstable position. I like the big moves where I expect to come off, but it just works. I like the cheeky heel hook which turns a struggle into a saunter. The blind reach to a thank God hold. I like to look up at it and say "that was fun" or "next time..." Or "how the hell !!".
Maybe indoors I like the failure more than the success. Once I've cracked the puzzle, the novelty is mostly gone, so the good move must be really good to get me to repeat it.
Being short and fat, huge reaches just annoy me. If learning technique will bring the hold easily within reach, then I'm more than happy.
As a punter, or am I a bimbly nowadays, I accept that what I look for may be different to what others would like.