I LOVE Myrtle Beach. My boyfriend and I have gone the last two years for New Year's. North Myrtle tends to be a bit quieter. When you get into the heart of Myrtle Beach (Ocean Blvd area), there is a TON of stuff to do.
As PP mentioned, Broadway at the Beach is a must. It's sort of similar to DTD. It's one main complex that circles a lake. One side is comprised of a variety of different shops. Then there's an entire section of restaurants, and another part has all the "attractions"...MagiQuest, a mini golf course, WonderWorks, and the Ripley's Aquarium.
On the Grand Strand, you'll find the Ripley's Believe it or Not Museum, some haunted attractions, more shops (check out the Gay Dolphin Gift Cove...it's like a 5 floor gift shop), arcades, and more. There's also a small amusement park called Family Kingdom. Plus, you know, the actual beach itself. Oh, and another fun thing is the SkyWheel...it's an enclosed glass Ferris Wheel. I think it's $13 for a ticket, but you get 3-4 revolutions. If you catch it just right at sunset, it's absolutely beautiful.
ETA: Forgot to mention Medieval Times. It's a dinner show with knights and a royal family. A bit on the $$ side, but it's good corny fun (or at least, corny for anyone over 10)
Go to visitmyrtlebeach.com. It's the official tourism website for Myrtle Beach, and it lists a lot of the attractions, and you can even print off a coupon book. This book includes a lot of coupons for restaurants, but it also has some that offer a dollar or so off the main attractions.
Hope this helped!