I just got back from there and I am headed back in June, great spot!

As far as courses, Harbour Town is the crown jewel however I prefer Oyster Reef, Jack Nicklaus Indigo Run, and Palmetto Dunes Courses. I would avoid Shipyard.

Harbour Town isn't as pricey as you might think. If you play in the afternoon there is a rate drop. I think that is the best time to play it anyway. But if you can't swing Harbour Town here are my next best suggestions:

Dafuskie Island: Melrose - You have to take a water taxi over but you basically have a really good golf course to yourself.

Sea Pines: Herron Point - Go see the clubhouse and the 18th is a great hole.

Palmetto Dunes: Jones Course - One of the few holes on the Atlantic Ocean that you can get access to.

Those are the public courses I would suggest.

Hilton Head National is a nice, affordable track and a favorite we play every year. Golden Bear at Indigo Run is a nice layout, but conditions can be hit or miss. Eagle's Point and Crescent Point are decent and offer good deals. If you have any college age or younger players check with the course often they will charge their age for a round as long as they are with a full paying adult.

I am with you on HH National. Always in great shape. Scenic. No homes bordering it. Love the Weed nine!

I've been going to Hilton Head since a young boy as a large part of my family retired there. I've played a few times in Bluffton (off the island) and a handful of courses on the island. Last year we played at the Arthur Hills course in Palmetto Dunes, which is a community with a great collection of courses. Best of the three probably being the RTJ course. The community where Harbor Town is located is called Sea Pines. I haven't had the chance to play anywhere in that community yet, but there are two other courses other than Harbor Town worth playing. Also played the Golden Bear course on the island, but I would start with any of the courses in Sea Pines, or Palmetto Dunes.

I enjoy the three Palmetto Dunes courses. The Jones course has a hole on the ocean and is my favorite of the three. You should really try to play Harbour Town. It is worth the money. Heron Point is also nice.

You can't go wrong with the Palmetto Dunes courses and having played the Jones course multiple times, going long on the ocean hole brings a whole new meaning of playing it from the bunker! LOL! The Fazio course there is usually not too crowded and allows for a fairly quick round.
The re-do of Heron Point is a must play as well.
They usually have some decent rates at that time too.

Enjoy and watch for the gators!

You already are getting a lot of good suggestions. Avoid Shipyard and Port Royal. Palmetto Dunes has several good courses. I like the Arthur Hills course. Oyster Reef at Hilton Head Plantation is very nice and challenging Reese Jones design.

If you're a member of a Private Club, you can check with your PGA Pro to see if he can get you on any of the private courses like Long Cove, Belfair, Colleton River or - for a true caddy + golf experience - Chechessee (a great Coor/Crenshaw course)

We played a couple of rounds there last year on our way from Orlando to Myrtle. We hit Old South and Bear Creek. Loved both courses. Coming from Denver seeing a tree lined course was a nice change. If I recall the greens at Bear Club we extremely fast but rolled very nice.