Ponza is an island destination mostly frequented by Italians (especially Romans and Neapolitans, as it's just a hop, skip, and a jump away by boat) that is largely undiscovered by foreign tourists. In some months of the year, you'll find it's empty, with just the relatively few locals who stay year-round. In the high-season months (May-August), you may find it packed with vacationing Italians, mostly families, couples, and groups of friends in their teens and twenties.
Since it's such a small island, Ponza doesn't offer a whole lot in terms of nightlife, so you should go prepared for some laid-back evenings out. Take a post-dinner stroll around the port in your nicest outfit, Italian style, while you enjoy a gelato and browse the souvenir shops that are open until late. If you're up for a drink, have a seat in one of the bars right along the water's edge and sip your cocktail while the soft sea breeze soothes your sunburnt skin.