Paros in August

No, a week is not too long. You can visit the small island of Antiparos. Also the cathedral in Parikia is amazing. We rented a car and drove around the island plus went up into mountains to Lefkes.. Two trips to Greece for a month at a time and Paros is my favorite island. (Loved Chania, Crete but Crete is so large I don't put it in the " Greek island" category.) Napflion is our other favorite place in Greece.
Enjoy Paros; it sounds like a perfect trip.

You can take a little local shuttle ferry across to Antiparos for the day. The one from Parikia's main dock takes about 45 minutes. The one from the little port of Pounta takes 10 minutes (and it is very frequent), and on that one you can take a rental car or scooter with you for very little money.

I highly recommend a full-day boat cruise called a Lazy Day with Captain Ben. He starts in Antiparos, and then stops at Pounta on Paros to pick up more passengers there. The boat stops several places for swimming and snorkeling, and there are drinks on board, plus lunch. It's very safe, spectacular scenery, lots of fun. You might need to reserve in advance for August.

Captain Ben sounds good, but if you cannot book him, there are a number of outfits that do the same thing. There is also kayaking off antiparos.

& there are several pretty beaches by short boat ride from Naoussa harbour, for just a few euros, check the wind direction before making your selection. We enjoyed Monastiri beach this June, super clear water, very shallow entry so takes ages to be deep enough to swim in, but safe for kids.

Thanks so much everyone for your helpful responses!