First, most of Hilton Head is divided into different Plantations, which are semi-private or private communities. Many of which you need a security pass to access.
The hotels are nice if you looking at staying a couple of nights, but the nicer ones are going to cost you. I recommend the Crowne Plaza (Shipyard Plantation) or the Westin(Port Royal Plantation). Although you have to make a trip to the Tiki Hut at the Holiday Inn.
If you are staying a week I would definately recommend looking into renting a villa/condo. You can either rent directly from the owners or there are a lot of Rental Companies. Palmetto Dunes Plantation has the most rentals of villa and condos, from golf course views to oceanfront. The plantation also offers 3 golf courses, restaurants, tennis, bike rentals ( a must do on Hilton Head), fishing in the lagoons. palmettodunes.com is the company that has an office on site and has the most availablity.
Just make sure to read the fine print on rentals. Many have extra fees for cleaning, you have to pick up the keys at a different location, etc.
I hope this helps, there are so many choices on hilton head, it is hard to decide what is best. All 12 miles of beach is wonderful, so if that is what you are going for it does not really matter what part you pick. Feel free to add another post once you narrow down what you are looking for and I will give you any input I have.
By the way I am a former Hilton Head Native and both my husband and I have worked at different Hotels & villa/condo companies on the Island.