We've yurt-camped at Devil's Lake. It's a campground within a city - which is kind of odd, but nice if you want to save money on accomodations, and have easy access to the beach!
It's on the eastside of hwy 101, but there is a path that takes you under 101 straight to the beach, so you don't have to worry about crossing 101 with kids, watching out for cars, and all of that.
Devil's Lake is not one of the more scenic or even relaxing campsites (because it's in a city), but it can be a good place to stay if your main priorities are saving money and being a short walking distance from the coast.
If you're interested in staying at a state park - Beachside might be a good option. It's right on the coast, on the westside of 101, with very short walking trails down to the coast. You have views of the ocean from many of the campsites. Your kids would love all the little bunnies that you see when you're there, too! There are some places along the coast where there are just tons and tons of cute little bunnies hopping around, and Beachside is one of them! (Sunset Bay and the area along Cape Arago hwy is another... that's among our top five favorite areas of the coast...) It's also not a very big campground, which feels nice. The beach at Beachside is very flat and sandy. We found sand dollars there recently. There are yurts there as well. Oregon State Parks and Recreation: Rates
Beachside isn't too far from the Oregon Coast Aquarium, either... about 15 - 20 minutes up hwy 101.
I've heard Beverly Beach and South Beach are nice, too, but we haven't stayed at those yet. They are also not far from Newport.
Any of these campgrounds are going to be busy and crowded during the summer months, when school is out and more families are out on holiday - especially on weekends. You might want to try to schedule your trip either in late spring or early fall if you want to miss some of the crowds... and also plan your stay during the week, as the weekends are the most busy. And remember that just because it's a beach, it's still Oregon - it can be very chilly... so bring warm comfy clothes and sturdy shoes. Our coast isn't a flip-flop, bikini-wearing kind of coast. We wear Bogs boots or hiking boots, jeans, and layers (t-shirt, light sweater or fleece jacket, a weather-resistant outer shell...) when we're there - even in August.
We do bring flip-flops with us but those we only wear back at the campsite when it's time for hot showers! I just have this thing about bare feet in public campground showers... so we wear flip flops...