Temperatures can be pleasant in the southeast US during the Spring Break months. Sea Island, for example has average high temps in March of 70°, 75° in April, but of course days vary; early March highs swung from 65 to 81°. Evenings are cool and ocean temperature averages 66° in spring.
(Generally, "spring break" for families in the US and Canada means a ten-day school-break in March or April; dates vary in different areas. College age spring break is a very different thing.)
Looking for affordable options? See: Family Spring Break Vacation Deals.
Myrtle Beach is on the coast of South Carolina, 98 miles north of Charleston; South Carolina is the #2 state for tourism after Florida. Myrtle Beach has 60-mile stretch of beaches (the "Grand Strand") and great fun parks for kids. Mid-March annual Canadian-American Days stage some special events. Note, however, that Myrtle Beach is also popular for college spring break! Families should check their hotel or resort carefully to make sure they're not amid springer-breakers: many properties have "over 21" rules for booking rooms; also, read visitor comments for last year's spring break weeks.
Fifteen miles from Atlanta, 3200-acre Stone Mountain Park is Georgia's number-one tourist draw, combining natural attractions (woods, lakes, and the famous "stone mountain") with man-made amusements such as sky ride, scenic railroad, laser light show. It's the largest outcropping of exposed granite in the world, and even that has a man-made attraction too: the world's largest sculpture carved into the stone (a gigantic Confederate Memorial.) Stone Mountain Park has an annual week of Spring Break Fun in early April.
Indoor water park resorts make great drive-to family getaways. This one is the Southeast’s "largest indoor and outdoor waterpark resort" (at time of writing - there's always a new "biggest" one); families like the tube slides, tots area, wave pool, surfing, and Runaway Canyon 450' waterslide with tunnel thrills, 360-degree loops, and water curtains. Location is in Sevierville on local Highway 66, "the gateway to the Smokies".
About.com's Guide for Southeast US Travel has suggestions for spring trips, including some big names in upscale travel, such as The Sanctuary at Kiawah Island and The Homestead, in the Allegheny Mountains of Virginia. Families who like indoor water park resorts will be glad to hear there's a Great Wolf Lodge in Willimamsburg Virginia.