I would use another isle vs Hydra -- It is endlessly hyped by Steves because i t's part of one of his tours, or is an add-on to a mainland-only tour... because it's a day trip. Beautiul harbor, a longish sea trip in enclosed-cabin ferry. No beaches handy, no cars or local transit except mules.
Instead I always recommend a day-trip to AEGINA... only 1 hr from port of Pireaus, and you can get a large OPEN-DECK ferry, you can enjoy the seascape... see huge liners, freighters, ferrries, schooners, speedboats, & shoreline... a little mini-cruise. When u arrive at port town, can explore small lanes, shops. You can rent a car for half a day, or take local bus/taxi OR (even better) rent an e-bike to center island hi hill & stunning Temple of Aphaia, 360° view of Saronic Bay... from there, a downhill "shortcut" takes u to Ag Marina beach village for lunch, & and a swim. Return to seaport for late-day cocktail in seaside cafe. Here's interesting detail step-by-step photo-log ol a daytrip - https://www.flickr.com/photos/36264706@N03/sets/72157621604646139/detail/
TIP #1 those open-deck ferries are less frequent... usually 8:30 am, around noon & late-day. Check a ticket-office near your hotel to make sure you get right ferry. To get to port of Piraeus by 7:30 (go on board for coffee) take a 30 minute Metro ride on either Blue Line or Green Line; ask your hotel where to catch it & about the machine-tickets. The last returning open-deck leaves Aegina 6-ish pm TIP #2 - WHEN you are going makes a big difference (NOte for future -- it's thoughtful to give key info when asking for best advice). In summer, this island crowds up on weekends with Athenians ... so you do better going M - F.