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Hilton Head Island : things/places to do there for 2-3 days
October is a great time to visit Hilton Head Island since the summer (tourist) season is over and it is not as hot and humid. My recommendations would really depend on what you want to do - beach, dining, golf, nature, nightlife, culture, history, etc. It's also festival season, so there is a festival nearly every weekend and the locals come out of hiding!
It also depends on where you are staying, since HHI has several gated communities (like Sea Pines and Palmetto Dunes). For instance, you can get into Sea Pines to go to Harbour Town (where the candy-striped Lighthouse is located) and go to The Salty Dog in South Beach Marina, but it costs about $8 for a gate pass (and an additional fee to climb to the top of the Lighthouse).
Local tip: if you like bike riding, you can ride the 12 miles of beach, as well as miles of paved pathways across the Island. All of the beaches on HHI are public and you can bike into many of the private communities if you pedal through a beach access rather than the main gate.
Coligny Beach is on the south end and is easily accessible and a big tourist destination with showers, restrooms and the Tiki Hut with drinks, live music and beach volleyball. On the North end of HHI, Burke's Beach less touristy, and Mitchelville Beach Park or Fish Haul have more birds than tourists, although to get to Fish Haul, it's a hike through Mitchelville Preservation Park and the maritime forest.
Hope that helps! If you let me know what you are interested in seeing and doing, I can give you more specific tips.