No No no, NOT a good idea! You essentially have three days in Athens (25-26-27) and you'd spend all day from early morning until late evening getting to Mykonos & Back, with maybe 1=2 hours on an island that's not even "open for business"!
Instead, why not enjoy the spectacle! March 25 is Greek Independence Day, celebrating the brave uprising in 1821, led by a priest who raised the Greek flag in defiance of FOUR CENTURIES of Turkish conquest, occupation and oppression. The Greeks celebrate their Independence day with far more than we bring to July 4th, having been conquered so many times and for so many centuries (essentially 100 BC - 1900 AD!). There will be a big parade in Syntagma Square, lots of flags and music -- and then yes you can go to the Acropolis museum, enjoy a wonderful (and v. mod. price) luncheon in its glass-enclosed terrace restaurant looking up at the Parthenon. Prep yourself before the Museum and ask questions of the "docents" that are standing around... and you'll prepare yourself to visit the Acropolis on 26th, in AM .. and the Ancient Agora & much more!!
This handy map - http://www.planetware.com/tourist-attractions-/athens-gr-ath-ath.htm#GR107 - (click to enlarge, & print to take) shows how close all landmarks are ... Temple of Zeus, Hadrian's arch etc. Stop at a sunny outside taverna for a souvlaki lunch! March 26 is a Thursday & the superb Benaki Museum is FREE that day, and open until MIDNIGHT! A delight, SO compact, 4,000 years of art & history in brief, with GOOD signage. BONUS: a lovely cafe where you can observe chic Athenians at lunch or fllirting over cocktails. This handy list http://www.athensinfoguide.com/open.htm shows sites, locations, hours of Dozens of wonderful attractions; A Jewelry Museum! A Musical Instruments Museum! Do u admire that gorgeous Actress - Patriot Melini Mercouri, who helped overthrow a dictatorship, then became Minister of Culture! There's a Foundation with a thrilling photo-display of her life works. I've enjoyed ALL these and more; have your hotelier mark them on a map, don sturdy shoes and you'll have a day of joy.
If you still have energy on day #3 and feel you want to see ONE island, take a Green Line Metro (€1+) or a taxi (€15-20) to the port, Piraeus, and catch a 1-hour ferry to AEGINA (NOTE: take a ferry with open decks, NOT a hydrofoil, which is enclosed, no views). U can enjoy all the shipping in lovely Saronic Bay. On landing, stroll the town, catch a bus or take a taxi 15 minutes to Mid-island to see THE most perfectly-preserved Temple in all the islands --- Temple of Aphaia on hi hill, stunning 360° view. Hike downhill to little seaside village of Ag. Marina, have a bite of lunch, bus or taxi back to port, and catch a ferry. An island "taste" in a few hours; here's a photo album of a June day-trip there: https://www.flickr.com/photos/36264706@N03/sets/72157621604646139/detail/
Rick Steves website has a good FREE audio download of a D-I-Y tour of Acropolis AND ancient Agora ... and it's in his guide book too. His new book may even have D-I-Y tour of Acrop. Mus. One last note about being prudent: if you are in the Syntagma Square crowd for festivities, or take a Metro to Piraeus -- Leave valuables, tickets & passport locked in your luggage at hotel & only take a change purse with your money for the day, zipped deep inside your day bag. Athens has FAR less pickpocketing than the other Europe capitals, but the 2 places that it occurs is in busy Syntagma square, and on the metro to the ferries. (PS: most tourists who are pickpocketed are MEN; women are used to being alert about their handbags).
All the above is from a female who often travels alone in Athens, loves it, feels safer than in any big city I've toured or lived in (I'm now in Philly, spent 35 years in NYC). You'll have a wonderful 3 days!