That's a bit of a 'how long is piece of string?' question, because there are multiple ways to do such trips. Broadly speaking though, if you get direct flights to the US in the summer or to Costa Rica in the winter or to anywhere long haul in high season, yes you will pay thousands for four people. Your exact travel dates, airline and routing will determine exactly how many thousands. You can reduce the price by flying indirect, using budget airlines, shopping around, setting up price alerts via skyscanner, using airline sales, using air miles (if you have them), etc.
As for accommodation - you can stay in budget hotels or motels, self cater, airbnb, etc and that will massively reduce the price of a holiday that can easily run into multiple thousands. Joining airline, hotel and restaurant chain loyalty schemes can also save you quite a bit if you do your homework. Unfortunately, being stuck with school holidays does limit how tightly you can budget on a big ticket trip and yes, the price will run into thousands, but whether it's £8k or £15k or even more is within your control.
With regard to Costa Rica, the main problem in terms of cost is that there are very flew airlines that fly there direct from the UK, so if you want direct flights there isn't a lot of competition to keep prices down. We found it a really expensive country too - eating out, activities, hotels - all UK/US prices. It seems they have two prices there - one for the locals and one for tourists and the tourist prices are high.