A totally non-diving experience on Roatan?
Get an English speaking guide/driver. Not just a cabbie, but somebody who has been on Roatan for quite a while.
You'll do the usual stuff (seaplane rides, submarines, golf, the chairlift, etc). However- here's some of the other ways:
Have him drive you to Oak Ridge. Hire, with him, a water taxi for the day. Cruise up and down the far East End of the South side, stop at bars on stilts, see the inter-coastal that has been sliced through the mangroves.
Or, have them take you by water taxi panga further East to where the Pirates truly stood- Port Royal. You can poke around, look at abandoned wrecks, or maybe even take the mangrove channel cut through Roatan to it's North Side.
You may want to set foot upon Isla Helena or Morat... most people think they are pieces of Roatan, but they are indeed different islands! If it is very very flat and calm, you might want to head for Barbaretta- I have done this in a Panga- take precautions for Sun exposure and take water!
Very good snorkeling available from the shore entry point of Fantasy Island. For a price, you can get in and have access to the showers, pool (if operational) a beach and the grounds. This shares the same dive/snorkel site with Cocoview, but FI sells day passes. Snorkel over to Cocoview, make a "beach landing", and go poke around. Bring a few dollars for the bar, Dollars will work okay when wet.
Stop at other resorts that are spread across the island. When people visit Roatan, they rarely go outside of the small segmented zone they rent a room within. I would suggest a visit to Reef House Resort- a little jewel which very few people ever get to.
A good source of first hand user reports:
http://forums.roatan.com/?forum=25272