Define a while? Last I knew, the Schengen area lets US citizens on the Visa Waiver program stay for a rolling 90 days out of 180. So, you could go for nearly six weeks before leaving, then once you stay out for six more weeks and some days fall off your ledger you can come back.

You can play games and leave the Schengen area but not go back to the US. The UK has its own requirements,and since you likely meet them you could go there and chill for six weeks waiting for your Schengen access to time out.

This all implies that you have the means during this gap year to fund it all yourself. If any country suspects you are working without authorization, they will escort you back to the US, albeit in a much kinder fashion than we are doing it to their citizens.