Those dates will be after the 2015 Heritage RBC Golf tourney, so the crowds will not be unusually high. There will still be a lot of families spending their spring break at HH. The weather in late April will be wonderful with temps in the 70's and low 80's. The ocean will still be a little chilly for swimming but can be upper 60's to around 70. Pools at the resort are heated though.
Dining options will be in full swing (there are very few seasonal closures at all any more at Hilton Head) and there are good options within walking distance of the resort and many, many more a short drive away.
Kingfisher, Scott's Fishmarket, Le Bistro, Little Venice, Parrot Cove, San Miguels and ELA's are all located around the harbor, an easy walk from the resort. Giuseppi's Pizza is about 1/2 mile and a new restaurant, Poseidon's, will be opening soon at the recently updated Shelter Cove Towne Center - also within walking distance. HH has about 300 restaurants, so there is truly something for every taste and wallet all within about 20 minutes by car.
Enjoy!