I'm assuming you are asking about undergraduate schools since you did not specify. University is not free or cheap in the USA, unfortunately this is a reality that you will have to deal with if you want to study here. Most schools offer merit-based (scholarships / grants) and need-based aid. Need-based aid may be hard to come by if you are not a US citizen (perhaps other users with experience can chime in). IMO for undergrad financial aid will be the most important thing to bring down the price, so you should engage with the office of financial aid early at whatever colleges/universities you are applying to.

Public Universities tend to be cheaper, especially if you live in the state where the school is located. This is especially important if you live in a state with good public CS schools, like Illinois (University of Illinois @ Champaign Urbana is a top 5 program) or California (see the various UCs, including of course Berkeley). So if you are lucky enough to live in those states then that is a viable option.

If you win the admissions lottery and can get into an elite program (unfortunately it is a lottery, in many ways due to simple supply and demand, and I say this as someone in a top-ranked CS program), it's gonna run you up to $60,000 per year without any financial aid depending on the school. Many people will take out student loans to offset this cost, and with a CS degree it is easier to pay off the loans, but that is still a financial risk you need to consider.

Honestly, if possible, just go to school in the EU if you're an EU citizen. There are many great schools there and the cost of flying there and finding a house is likely lower than the tuition on this side of the pond. Many Americans would kill for the opportunity for a free education.