Lisa, I actually found my current tailor (who has been terrific) on Yelp, and he happens to own a dry cleaning business, but used to be a tailor in Hong Kong. I just want to say, please don't rule someone out just because s/he happens to have a dry cleaning business. Sometimes, depending on the needs of the community, s/he might need to do both to make a decent living.
But with that said, I've also had the bad experience of entrusting a garment to a dry cleaner who did alterations on the side to bring in extra income, but who was not skilled and did a terrible job. I think the bottom line is, ask around--ask your friends, neighbors, colleagues, even local strangers who seem to be well-attired--try the tailors who get 5-star reviews on Yelp, and as Mellllls suggested, entrust only one garment at a time until you feel you've found The One.
Last of all, I've found through experience that, Surprise! Tailors are human too. They're not magicians and aren't going to be able to succeed 100 percent of the time in transforming a garment the way you envision. I've found that it's important to communicate well about what I have in mind, ask about the cost up front before deciding whether to leave the garment for the work agreed upon, and most importantly, to take the time to try the item on when I pick it up to ensure that it fits properly and to ask for changes if it doesn't. I've found that a good tailor wants you to be happy to ensure that you'll continue bringing him or her your business and hopefully recommend that your friends do too!
Hope none of this sounds too pompous, Lisa--it comes from several years of good and bad experiences!