How do you define "high-end?"
We usually find "high-end" clients in middle to upper-middle class neighborhoods. We find them in blue collar and million dollar neighborhoods, too. "High-end" to me is someone who values quality and service over price, and values you as someone they want to call.
How you advertise is part of it. It's simply how you get your message in front of them. It's fair to say 75 to 85% of your business is repeat and referral so I think there's a strong argument that how you conduct yourself on the job is even more important.
Just MHO, but one way to attract them is to appeal to what they want: quality, service, value, safety, trust, reliability, professionalism and so on. Dress professionally, shave, don't smoke, arrive on time, call if you're late, look them in the eye, don't eyeball them, their kids or their stuff, talk about your wife, kids, family and pets, do the things you'd want from any guy who's gonna have the run of your house while you're out earning your keep. From the moment you arrive do things to put them at ease.
Everybody has a comfortable maximum they believe they can charge. Or, more correctly, what they think Mrs. Piffleton will happily pay. If you're like most of us it's based where you started and regulated by the fear of asking for more. One of the bigger things about attracting "high-end" customers, IMHO, is your own perception what your service is worth. When you allow yourself to charge what you perceive are truly "high-end" prices and sincerely see the value in what you do, the more your customers will value you.