I totally agree with Dick's suggestion in Paragraph #3. Get up early -- to Acropolis 8:15 to avoid the crowds, then walk down thru the Agora (BTW, the Rick guide has a great step-by-step tour of Acropolis/Agora), then to Acrop. Museum. Take a breather, have lunch in it's lovely glassed-in terrace looking up at Parthenon, then explore Museum... wander around Plaka, taking in some other sights (Hadrian's Arch, Temple of Zeus both good "walk-by", Syntagma square).
On day 2, after AM in N.A.M, you can do a D-I-Y trip to Delphi, IF you're willing to do some "homework" beforehand &have guidebook or internet printout for the ruins (the museum has GOOD signage) Here's good internet info (PRINT!) http://www.planetware.com/greece/delphi-gr-cen-delphi.htm#GR-CEN-DATHM
and here's a wonderful guide to DIY trip by Mariha, a professional in hotel industry who LIVES in Delphi:
-- it's VERY accurate with update shown: bus NOW stops at entrance to Museum/Ruins, and THEN proceeds to final stop uphill about 1/2 mile, at town Center. PRINT THIS & follow!
There IS an overnight trip, but probably wouldn't allow you to do the morning at the N.A.M.... and you'd pay a lot more. As Mariha suggests the best of both is to go D-I-Y & with the savings then hire prof. guide to meet you onsite. Here's the one Mariha highly recommends: http://www.delphi-guide.gr If u cannot afford the guide, here's the DIY that I've advised:
BUS: There's a bus at 10:30am & 1500 (3pm), so get lunch, then taxi (€11-12) from Museum to Liossion Bus Terminal. Bus (€15 each way) takes 3.5 hours (w rest stop) so it will be near sunset when u arrive. I recommend Hotel Pan on Main street... and any local taverna w. mtn view. In AM get up EARLY, at be at site 8 AM... if go to Museum First it's empty... then to ruins... bus groups don't arrive until 10:30. After main ruins site, walk downhill to Tholos tomb, castalian springs. Athens busses 11am, and 3 pm so u get latter.