I used to live in Hilton Head and go there at least once a month. I dont think you will find anything on or very near the beach without spending a lot, especially in April (think Spring Break and Easter). You might want to look into the Savannah/Pooler GA area. Ive stayed in Pooler just off 95 lots of times for school. The place is growing too. There are places to eat and hotels (I always stayed at the Microtel). Theres a McDonalds in front of that, and Cracker Barrell just across the street (and many more in the area). The Mighty 8th Air Museum is there too if you have the time and interest. I dont know how far exactly the beach is from there, but I dont think its too far. I believe its Tybee Island (think Ben Affleck had or has a home there).
Other than that, Charleston and Beaufort are nice, but not exactly right on the beach. Plus you will want more time to explore these places. The other thing, dont expect white sand and blue waters in SC and GA. The water is sort of a murky brown. The water will be chilly too in April. Hope this helps a bit!
alison