Italy Recs (Puglia vs Sicily or somewhere else?)

Hello! My wife and I are planning our honeymoon and are torn between Puglia vs Sicily or even somewhere else in Italy. We are in our young 30s and we will have roughly 5 or 6 nights (we know it's not a lot of time…) before heading to Greece (Naxos + Paros). Planning for the end of May.

Things we're looking for:

– accessibility to day trips

– accessibility to nice beaches (bonus points for any fun day clubs)

– somewhat affordable (or at least not very expensive)

– lively nightlife (not talking nightclubs – we're not clubbing people – but more so fun bars open late-ish and overall lively atmosphere around town in the evenings)

– interesting history/culture

– and of course, great food and drinks

We're slightly leaning towards Puglia although not sure where in Puglia, so any recs are appreciated.

We're also open to other ideas outside Puglia or Sicily! And of course any overall tips and thoughts are appreciated.

We'll likely fly into Rome from the States if that matters.

TIA!