We love Hilton Head and visit a couple times a year. We like to rent a villa in Palmetto Dunes Resort. Within the resort, we like the villas at Queens Grant.....very large...ground level with a deck and about an 8 min walk to the beach. it is mid Island so it is centrally located. We like Queens Grant because some of the units are pet friendly and we can bring our Cocker Spaniel. Anywhere in Palmetto Dunes is great. We always rent through home away or VRBO.com.
If you don't care about staying in a Plantation, Hilton Head Beach and Tennis Resort is right on the beach
and very affordable.
For a budget rental with great beach access, Hilton Head Resort has villas for about $700 a week. It is an older resort, but they have made improvements and the beach itself is beautiful. ThEy also have an indoor pool...not fancy at all...very basic, but nice for little ones if weather isn't great. The units are small, however.
Disney does have a resort here, but be aware that it is NOT on or near the beach per say. They do have a shuttle that will take you to their beach pavilion in Palmetto Dunes Resort. But you can rent a place yourself right in Palmetto Dunes and be closer to the beach for a lot less money.
There are bike trails all over....golf and tennis courses and tons of shopping, horseback riding, zip line, boating, fishing, etc.
Hilton Head is also easily accessible to Savannah and about two hours from Charleston.
If you rent through home away or VRBO, you will most likely pay less than renting a timeshare week. We have never paid over $900 a week and have stayed in some great places.
Hope this helps!! Have fun planning!!