More "classy" retro reprint than "classic"...I would recommend you visit (in person or online)
Newt's At The Royal Hawaiian. You can not beat the quality of print, fabric, and sewing construction of these truly fine aloha shirts. He purchased the old Kula Bay shirt company many years ago and added many new items since then. Very expensive but worth it. One-of-a-kind shirts from a one-of-a-kind shop. One of my favorite shirtmakers and I've been purchasing shirts from him (or Kula Bay before he purchased them) for over 30 years. My 30 year-old aloha shirts look and wear just like the day I purchased them.
Also up there in quality (but also in price) is
Reyn's (also known as Reyn Spooners). Another great line of retro and original aloha apparel available in several stores throughout the islands and via the web site. They even do especially creative Disney aloha shirts under a special license (newest release are some cool shirts based on "The Incredibles"). Reyn also custom makes shirts and logoware for some of the employees of many of the best resorts and restaurants in the islands.
Also high in quality but much more commercial, is
Tommy Bahama's. Most of his prints are new designs but many are done in retro style and they are very nice.
Hilo Hattie's is sorta the K-Mart quality of aloha shirts in my experience and opinion. They are
the mass retailer of aloha wear in the islands. Inexpensive and fine for what they are. But the quality of workmanship is not that great, IMHO. Also the designs tend to be a bit more limited (and some say "tacky") for my tastes. Not trying to be snobbish. It's just that Hattie's not my cup of tea I guess. But if you want some inexpensive aloha shirts that you don't plan on owning or wearing very long...they are fine.