When will you be going? There are different things to do at different times of the year.
If it's during the summer, hanging out at the two pools or the beach is always an option.
Other things are shopping, shopping, and more shopping. (Oh wait, you said you wanted
inexpensive things to do!

) Seriously, there are great shops all over the island (not just tourist traps, although there are enough of those too). There are outlets in Bluffton.
Go to Sea Pines one day and climb the lighthouse for a great view of the entire area. The Coastal Discovery Museum is a great idea.
I can't post links to websites yet, but hopefully you can find what I'm trying to steer you to for more general info about HH:
hiltonhead.com
hiltonheadisland.com
islandpacket.com

Sitting on your porch relaxing ain't too bad, either!