Is that near memorial day weekend? If it is i agree with the previous posters who recommended staying clear of Myrtle beach itself. Everyone getting in their last summer hurrah on top of the Atlantic Beach bike rally makes traffic INSANE!
Staying south the Myrtle Beach would probably make for a more enjoyable (and more reasonable) vacation.
Everything is very close together, starting from Myrtle beach and heading south there's Surfside Beach, Garden City, Murrell's Inlet, Litchfield and Pawley's Island. They all have their charm and Surfside, Garden City and Murrell's Inlet are so close you don't know when you leave one and enter the other.
I live in Surfside Beach, just south of MB and I'd recommend staying here. There's plenty of hotels and there's also beach houses for rent (google them, there's a bunch - i'm not sure on how the prices compare to hotels).
As far as cheap things to do. This area seems to be the putt putt capital of the world. You can blow a half a day on that and many places have options to play all day (come and go privileges) for a reasonable price.
There's racks of coupons and discount books at most restaurants, hotels and convenience stores. Definitely grab a handful.
Someone mentioned Sam's corner and the arcade next to it. The arcade is big fun for kids. (the Sam's corner and arcade I'm talking about is in Garden City - tiny bit south of Surfside). It's huge and a fairly old school arcade with skee ball, air hockey, all kinds of video games and you can win tickets on lots of the games and trade them in for toys and, well, junk but kids love it. That Sam's and that arcade is across the street from the Garden City Pier, which also has an arcade. If you like to fish you can fish from the pier during the day. They used to have bands at night (free) but i don't know if they do that anymore.
There's a place called Maze Mania that is a maze made of wooden walls that the kids (and the adults if they want) have to find their way through. There's also an observation deck so you can watch the kids try and figure it out. Not a huge deal but not expensive.
There's a water park in Surfside. A show called Legends in Concert where you can see celebrity impersonators (not cheap but it is entertaining).
Surfside also has a pier you can fish from or just wander out on to enjoy the view. There's a restaurant on the pier called Nibil's. It's not fancy but it very reasonable and the food is very good. Eating breakfast there on the pier is wonderful.
The beaches will get less and less crowded the further south you go.
If you are from a state where fireworks are illegal (and you're comfortable doing this) you can stop at one of the fireworks stores and pick up some and shoot them off on the beach. i *think* it's still ok in Garden City.
Murrell's Inlet has amazing restaurants. Not necessarily budget friendly but amazing. Lee's inlet Kitchen has amazing seafood. Flo's is fun and funky cajun. Bovine's has great steak and wood oven pizza. Divine's has great fish and a great sushi bar. If you want a seafood buffet, The Admiral's Flagship has good food and is much better than the 'chain' type buffets.
Oh, there is a budget friendly restaurant in the inlet. Creekrats. It has indoor and outdoor seating. They often have a small band outside in the summer and dancing. Family friendly and the kids dance right with the adults.
Another vote for Brookgreen Gardens to seellovely flowers and awesome sculpture - and the state park across the street for beaches with NO crowds.
If you brave Myrtle Beach - Broadway at the Beach is great for shopping, IMAX, magicquest lots of shops and restaurants. The browsing is budget friendly - the stores and restaurants not as much.

Similar to Broadway there's a place in North Myrtle beach called Barefoot Landing. Cute shops, House of Blues etc.
There's a cool children's museum in MB. Lots of interactive exhibits. Cheap, too.
There's many, many cool bars and clubs. The beach bars are cool, Broadway has some fun clubs.
Lots of shows, Legends in Concert, Alabama Theater, Medieval Times, Dolly Parton's Dixie Stampede, the Carolina Opry etc. The previous poster who called it Branson on the beach was right.
As far as safety, you should be fine. If you're walking down Ocean Blvd late at night (not recommended) you'll probably encounter quite a few drunks but serious crime is pretty minimal. I'd be most careful about the traffic and accidents.
I've rambled enough.

If there's something specific you're looking for PM me, I'd be glad to help.