Already looking for work in EU, but want to also engage in tourism

I'm a US citizen in between jobs right now and also in a long distance relationship with someone in the EU. I've been looking for work in the US and the EU right now, and am hoping to get a job that will get me sponsorship. My potential job is in finance. I also miss my boyfriend a lot and want to visit him for two weeks.

What must I do to be able to do that? I can't be the first person who's decided to take an international vacation in between jobs. If I enter the EU, what are the rules regarding the job search? For example, if I get an interview with a company in the EU, will I have to first exit the EU, then reenter? What documentation should I bring to demonstrate that I don't plan to stay in the EU at the end of that visit? Would a return ticket, invitation letter, and a bank statement suffice?

I tried researching all this, but everything online just says that US citizens can enter the EU visa-free. Nothing specific to my circumstances.

EDIT for completeness: I've entered the EU three times before in the past three months for a week, a week, and a weekend. The ties that I have to the US are that my family lives there and I have a bank account there.