It is approximately 5 hours from Orlando to Hilton Head. You will need to take Interstate 4 East out of Orlando. It will connect with Route 95 (you want 95 North) and that will take you all the way to South Carolina. Take Exit 8 in South Carolina (it is just 8 miles after you cross the Georgia/South Carolina border) and follow the signs to Hilton Head. It is apporximately 30 miles from the highway to the island.
We don't find it tiresome at all...but then again we are used to driving straight through from Connecticut to Orlando (about 20 hours)!
If you are driving during the week I'd try to leave Orlando before 5am, between 9am and 2pm or after 6pm. That way you will beat the rush hour traffic in Orlando and Jacksonville.
Have fun!