Here's the current version of the rule being considered in the EU ... it's possible it'll change by the time it is adopted (I expect that there will be some relatively minor changes based on today's news):
https://ec.europa.eu/home-affairs/s...al_council_recommendation_com-2021-232_en.pdf
That version lifts the ban on nonessential travel only for vaccinated individuals with no allowance for testing or quarantine as an alternative. The EU will also allow admittance of unvaccinated individuals from countries that have low risk of COVID infection (like Australia ... the US may eventually get there but our case rate is about 2x what is allowed). It is possible for an unvaccinated individual to enter with testing or quarantine if they are considered to be traveling for an essential reason, but not for tourism.
Individual countries like Greece have adopted rules that are less strict than the EU recommendation (and they still have that option), but unless changed the EU recommendation wouldn't allow unvaccinated individuals from the US (except children ineligible for the vaccine who are accompanying vaccinated adults) to enter for tourism.