I've spent time in OC every year of my life and I'm cheap, so I've got lots of ideas.
I second Northside park and fishing is lots of fun. There are quite a few "free" fishing spots around town. I've got a list of them on another computer if you're interested.
If you google "Ocean City MD free family fun", you'll find their tourism website with free movies on the beach, concerts, family olympics on the beach, etc. Some of the concerts are at Northside Park and you can purchase ice cream sundaes to eat while you listen. As I recall they are not too expensive.
The Carousel Hotel has an ice skating rink in the lobby, and once a week a professional group from Baltimore (I think) does an ice show that is great and free to watch (get there a little early). I think it's Wednesday evenings, but definitely check. They are really good and very popular.
We love the boardwalk, which can be crazy expensive, but if you go to snack a little, window shop, listen to the musicians, and people watch it's great fun. Farther up the beach (North of 1st Street), they have big play equipment on the beach which my kids loved when they were little.
And of course the best free thing is the beach! I could spend all day there. We walk, swim, sunbathe, collect shells, and in the evening fly kites. Northside Park is also a good place to fly kites. You can pick up a couple cheap at Rose's. Fishing gear too.
If you don't mind a little drive, go to Assateague State Park. I think it's $15/carload to get in, there is a beautiful and much less crowded beach, and if you are lucky you'll see the wild ponies wandering around. I think they have special nature programs for the kids.
On the way back from Assateague, we stop at Frontiertown Campground on Rt 611/Stephen Decatur Highway. It's not just for folks camping there. You can get unlimited water park and mini-golf access for a day for $14 for adults, less for kids, which is much less than you'll pay in OC. Look for coupons too. The water park is not huge but has 4 big slides, a big themed kiddie pool, and a lazy river. It's enough to keep my kids (middle schoolers) happy for 2 or 3 hours. The little restaurant next to the golf and water park is decent and has specials and alcohol! We never do the Western Theme Park because it seems kind of hokey but little kids might like it.
As for food we stay in a condo and take turns cooking so we don't eat out much mostly because we prefer it that way. But we always get a giant 28" pizza from Captain's Pizza. They have to turn it sideways to get it through the door and the kids get a real kick out of it. Pricewise not too bad as it feeds a ton of people.
I hesitate to tell you about this next one, as I love this place and would be devastated if it changes: Rippons Seafood at 11911 Coastal Hwy (tucked behind a 7-11). It's a carryout seafood place, and it's high quality stuff, not the junk they're feeding the tourists. I can get crabmeat like I remember it there (the stuff that only goes to the expensive restaurants now). I make better crabcakes than any restaurant around so we buy a couple of pounds and some shrimp and have a seafood feast in the condo one night for much less than a restaurant (and much better too!). They have lots of prepared stuff.
The Minit Market on 33rd and Philadelphia is a little hole in the wall place with a real butcher shop, but the most awesome thing about it is the doughnuts they make fresh every day. Get there early because they sell out, but they are worth it, super yummy and hot from the oven. Go straight to the back of the store and get in line. They are not the raised kind, but the cakey kind, great for dunking, and my favorite is the cinnamon sugar.
That's all I can think of right now! I always told the kids we are there for the beach, not all the touristy stuff, and we always manage to have a great time! We could go anywhere else we wanted for a summer vacation, but the kids always want to go for their OC week. We'll be there for a week in July. HTH and have a wonderful vacation!
) that is on the other side of the road from the beach, has 2 double beds that have to be 40 years old (could not sleep on them), mini fridge and stovetop, and he is paying $620 for 6 nights. We are going to be ocean front with a balcony, 2 room suite (bedroom with 2 doubles and living room separated by the kitchenette with full size fridge and stove and oven) have 2 pools, a lazy river, and not have to deal with road traffic walking out to the beach for $570 for 6 nights.
You all are making me wish I was on the boardwalk pigging out right now. 
