When researching for my trip, I found out that many things in Greece, generally speaking, change opening times and availability pretty much April 1st. Not saying all the places but the ones I looked at, including the Acropolis, and most if not all Athens museums changed their opening hours. I do know places like Corfu and santorini tend to open more things up in April. Rhodes seems to be pretty well open "most" of the year, with the possible exceptions of hotels. This also applies to ferry routes.
I should add, that despite what some people may suggest is that the islands ARE worth going for day trips if that is your thing. For instance, I got round trips to rhodes and heraklion for 130 CAD. Roughly the same price as ferries would be. While you could easily spend a few days or even a week on any given island, even getting to see them for a day, IMO is worth it.
That being said, in Athens, everything should be open. You can also do day trips/tours to places like Mycenae and Delphi. For me it was just easier, and I usually dislike tours. But for convenience, it was an easy choice, especially delphi. Mycenae can easily be driven too, with tons of places to stop along the way, however id HIGHLY suggest renting a car outside of Athens unless you are VERY familiar with european drivers. Most places on mainland greece should be open with some slightly less hours open. Island wise some are basically closed until April, and some are less so, and some are pretty much open year round. I believe that most of crete will be fine and is an amazing place to see. Just beware that you could easily spend as much time there as you could on the Greek mainland. There is that much to do there especially if youre a history nerd.
I would like to add though, that mykonos and santorini are unfortunatly overrun with tourists and the "old" days of it being a peaceful chill place are long gone. This applies more in the high season, but from what ive read even in the low season it can get pretty busy, despite many things not being open. Some islands may not even have ferry routes running or severely reduced service and the only way to get to them is flying, again, with deduced service.
March IS a great time to see greece though. Its much quieter. A lot of cruise ships dont start till April or May. The weather is decent and many attractions might even have reduced prices to get into.