It's hard to say. Sometimes it's the design/pattern. Other times a bright color or fabric just seems to jump out. Sometimes it's the originality & great idea.

If I'm looking just for pleasure, I look at pattern first, then color, then if I really love it, the quilting. Who cares about the binding. If I'm considering buying, I look at color first.

It's usually color that grabs me first, and sometimes it grabs me in a bad way. If the colors clash or the overall look is just weird (to me) I don't try to analyze it any further, just kind of turn away mentally.
If the color is exciting, interesting or soothing, then I give a second look, and take in the pattern, quilting, and the general feel of the quilt. I would only notice the binding if it stood out in some way.

overall, color, pattern, quilting-----binding is a distant 5th! I've always heard that at big shows judges are very picky about binding as it can be a "deal breaker".

think it's like a woman dressed up--we notice overall, notice the dress (color), notice the fit(pattern), notice the quilting (accessorizing) and if we notice dirty nails it's like bad binding!

Honestly, I look at the quilting first, and the piecing, because I like to see if it is done by hand or machine. Then I look at the colors, pattern etc.

Being a LongArm quilter, I usually look at the overall quilt then get up close and look at the quilting.

I look at the pattern and try to figure out how it is put together, then I look at the colors and think about how different colors would effect the overall look, and also consider ways to make it easily. I do look at bindings, just to see if they've used a technique I don't know. I am an engineer, so I'm always more interested in how things are put together just by nature.

My first thought when you mention people looking at the binding before seeing the quilt is that these are the same people that upon entering a house, they check the top of the door jam for dust instead of being happy to visit the people. I would prefer not to know those folks!

Same here and am always impressed with the amount of work that went into it whether by hand or machine. I despise quilt police. Spent the last 2 weeks with my brother and his wife. She had a friend who was looking at an older quilt that belonged her mother made for her when she turned 13 as she did for all her girls when they turned 13. I saw the beauty and the love that went into it. Her friend (?) pointed out ?flaws?. I told her those were her mother's signature imprints of love. ALso told my sister-in-law not to allow quilt police in her home again. Rudeee!!!

I get an overall impression of the quilt, then look at the pattern, then the color. I like to know how they are made (I, too, am an engineer) then see if I think I would be able to replicate the pattern.