And I don't mean the kind who court anyone and everyone. Not wanting to do this on the cheap. Also not soliciting. Thanks.
You have to be more specific. "Classy" means something different to each person. The dictionary definition is "stylish and sophisticated," and again both of those words are entirely dependent on your sense of what is style and what constitutes sophistication. Given that the only things you've specified is that you are willing to pay for time, not sexual contact, and that he or she should be selective, it's not much to go on. You don't even specify whether you are male, female, or other, nor whether you are seeking someone who is male, female, or other. The idea that you are "not soliciting" doesn't need to be said here. That no one is offering or asking for money for sex should be explicitly stated in advance by both parties (escort and client) unless your idea of fun is a police sting operation. My recommendation is that you ask someone you meet in your regular life activities who strikes you as classy and falls within your own concepts of stylish and sophisticated out on a date. Yes, in asking someone out on a date, you are offering to pay for things like a meal, entertainment, parking, and tips, and likely to provide some transportation. Because you're a free spender, make it expensive entertainment or an expensive meal. The only thing you aren't paying for is the person's time. Because you want a selective escort, someone likely to turn you down because he or she is turning down others, that's no different from dating. You may get turned down when you ask this classy person for a date - that's what selective people do, and what you say you want. You're making life more difficult than it has to be. Why go looking for someone "classy" to pay? Is someone "classy" going to be receptive to an offer to employ him or her for an evening out, and you're going to mention in the first 20 seconds that you're not paying for sex? There is absolutely nothing classy about your behavior in doing so. The first-chair violinist for your city's leading orchestra and who also speaks 6 languages and trained as an architect doesn't rent his or her time for dates, stylish and sophisticated though he or she may be. You've created a proposition of mutual exclusion, and set unreasonable expectations. Just ask out for a date someone classy you already know or the next classy person you meet.