last December i was in Greece for only 2 days, one day was for Athens, the second day I did a Corinth-Epidavros-Nafplio-Mycenae day tour. temps were in the 70's. i really did it just for Mycenae but the rest is very interesting too. it is a full day out, about 10+ hours.
you don't really see any of Corinth except the bridge you go over, the obligatory gift/food store, and the canal, but still worth the stop. walk back out on the bridge so you're standing over the canal for the best view of it.
Epidavros (nice little museum, if it's open) and Nafplio are interesting stops along the way to Mycenae.
as mentioned, Mycenae does have the Lion's Gate and it's archeological site, but also Agamemnon's Tomb on the way in, just down the road. all very, very impressive. something I've always wanted to see, did not leave disappointed.
you do have to buy a ticket to get into everything, so have some 50-100 euros each on you.
I'd like to do Delphi one day, but you won't be disappointed by a Mycenae day tour.