Hilton Head does have one Starbucks, but why go there when there are local options?
If you're looking for a spacious coffee shop to meet friends, read, or get some work done, Watusi is your best bet on the island. It serves tea, coffee, frozen yogurt, and breakfast in a quiet environment with loud and sassy signage throughout. They also sell some locally made kitchen accessories such as subtle beach-themed tea towels.
Watusi is conveniently located near the beach, so you can enjoy a cappuccino to go and then watch dolphins play in the waves.