The fav things I've done with non-divers at Catalina:
Interior tour - I've done most of the tours, but this was my fav. Not sure if they're offering this one any more. It was way, way cool. Long, but excellent. Winding up the road on a bus thing you just knew was going to fall down the mountain, then seeing all the stuff 99% of the people never see, getting to the airport in the sky, seeing buffalo and all kinds of things.
A real meal - skip all the restaurants in town and go to the Country Club.
A couple of years ago they opened for biz to non members, and its been the best thing to happen to Catalina dining. September is still warm enough - request a balcony table for two for dinner. Best wine selection on the island, and the only place you get cloth napkins, real table linens, real glasses (no plastic) real plates (no plastic) and a menu that changes weekly. Thursdays is Jazz night on the terrace. Best dining on the island. Be sure to get a reservation, and go early so you can sit in the bar for awhile. Check out the huge mirror behind the bar - etched with local fish and sea life. Its beautiful. Once inside the large dining room, order two or three appetizers and a couple of wine flights between the two of you and you're in and out for less than if you went to Stephen's Steakhouse with their terrible service or Anonio's with their paper napkins. Make sure you walk to the Country Club. Its a cool walk and takes you past the big pink hotel (the St Lauren)
Armstrongs - that said, have one meal at Armstrong's. Not ANTONIOS, Armstrong's. Mesquite Grilled fish. Order something off the grill. Its not cheap, and you'll have plastic on the table, etc, but they do an excellent job with the grill. I love the Samon or Halibut. Skip the unfortunate calamari sticks. Not good 'mari. Fish, wood, fire. Simple and excellent.
Snorkeling in Lovers cove - as you get off the boat, there is a big cove near the landing (what they call "the mole".) That's lovers cove. You can't dive it without special permission, but you can go snorkeling there. It gets pretty choppy, as its not as protected as the Dive park, but on a nice day its a pretty cool place to snorkel. Lots to see. Its where the glass bottom boats and that wacky yellow sub go.
Go to Two Harbors - its a little cow town up island about an hour. You can get a water taxi or other method (the Express hops over there a couple of times a week) and go see Two Harbors. Its small, its quaint, its rustic and its kinda cool as an extended day trip.
Take a Casino Tour - the building really is all that - especially on the inside. I love it, and whenever I'm there with a non-diver I go back again. Its beautiful inside and has a great history.
Catalina Tile - get a book or do some research on Catalina tile. Once you do, you'll never look at the town the same way again. Its like a treasure hunt full of tile going back 50, 60 years and even longer. There are tiles all over the place - some modern and many very, very old. Its a joy to walk the town and see them. I've only found one heart tile. I don't know if there are more - I've looked for years and only seen the one. The history of tile and Catalina pottery is really cool. Read up!
Courtyard Coffee - if you like coffee, this is the place. Make it your morning routine. Get up early, walk to Courtyard Coffee and watch the town wake up. Best coffee and espresso on the island. Get a paper and watch the sun light up the harbor. Its a great way to start your day. Don't worry, the crows will usually wake you in the morning (they're everywhere) but a walk to Courtyard, sitting by the fountain and watching the place change colors as the sun rises... one of my very fav things to do on Catalina
Dood - I could go on and on.
Catalina isn't a resort. Avalon is a little town with one and two-star hotels (the exception is the Snug Harbor inn...) but if you set your expectations to reasonable, and are ready for some alone time and want to dig in - its really, really a cool place.
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Ken