how does the primary schools system work in spain? (Barcelona)

Hello, we are moving to anywhere near Barcelona in the summer just to chill out for a few years. We have 2 kids which are 4 yrs old and 5 yrs old so would like know how the school system works ie would i have to pay for them to go to a school and if so how much does it cost.
We are not really looking to work so where is the best area to live to mix with like minded people that are interested in personal development which is what we want to spend out time doing and just chilling out.
So any tips or advice would be great.
I'm Irish and moved to London 20 yrs ago and married to a lovely English man that is a builder/plumber and he's happy to just take a yr or 2 off.