A major advantage of Aegina, besides being closer is that 2x a day or more (right now at 8:30am & 12:30) you can choose a "conventionai" ferry -- i.e., large vessel with open decks. Thus you can sit out for an hour & enjoy the "seascape" -- huge freighters, cruise ships, schooners, tiny sloops, shoreline etc. By contrast Hydra trips are all on Hydrofoils where u are stuck indoors in reserved seats, windows r salt-rimed no view. NOTE: Be sure to catch those open-deck ferries... the other Aegina sailings are hydrofoils -- I believe coming back, the last open-deck ferry goes at 18:15 or so (6:15pm).
Here's a wonderful photo-blog of a June dayttrip to Aegina (I need to thank its creator, because I've posted this every week for YEARS!) - http://www.flickr.com/photos/36264706@N03/sets/72157621604646139/detail/ it not only shows Aegina highlights, it shows the ferry trip over & back.
If u want to save time ticket-buying, the day before u could just purchase at any ticket agency near your hotel. A taxi during morning rush from Central Athens may cost €20-25... have your hotel clerk book taxi & confirm the estimate (no flat-fee for this ride). OR, if u are convenient to Monastiraki or Syntagma metro station, a Metro ride to PIraeus takes about 30 minutes... I'd plan to catch train by 7:15 or so, to allow time to find the gate. There's a coffee-bar on ferry, once you board.
TRANSPORTATION - You have several options, depending on budget & ambitions:
• Rental car options right at the port - don't know whether can do by hour or just by day
• At port, a bus stop w timetable. The main route takes you to high hill mid-island for famous Temple of Aphaia then onward. Problem is, if you get off at temple, that takes 15 mins, then next bus not for hours. What I did: walked down road 200 yards, saw handmade sign "shortcut to Ag Marina" (beach village). I scrambled downhill on dirt trail and presto! lanes leading right into Ag Marina... it was June, I'd brought swimsuit, so I used cafe restroom to change, had nice dip, and then had lunch at that cafe. I'd asked where/when next bus stopped & caught that.
• Another option is half/half. Before taking bus, stop at Taxi line to get cards from drivers w phone #. Ask them the est. fare from XX (wherever u plan to end up). THen, when wanting to return to port town, use cel phone to call... unless there's a taxi where u are.
• Final option: At port you now can rent "e-bikes" -- pedals with motor-assist. The road is good & not tricky, so if you're an experienced cyclist, this is ideal for you.
BEGINNING OF DAY - On arrival, right by pier is small ruins area... only ONE column (but u can take a tricky photo with it at one side, sea in background). Tiny museum; main items IMO were huge "man-size" ancient Amphora (jugs).
AFTERNOON - If u have time, coming back to port, it's fun to explore narrow back-streets; Aegina has lots of permanent Greek residents (many commute to Athens); I always love browsing in local groceries/ home decor shops for unique Greek brands. Then have a 5-oclock beverage or snack at seafront cafe - before summer, most other customers will be speaking Greek.