Is it worth it to take a day trip from Athens to delphi?
Yes, if there is one day trip which is worth doing from Athens, it is certainly Delphi! It is indeed a bit far from Athens, so I would recommend it to you only insofar as you are prepared to wake up relatively early, and travel for a few hours to go and return within the day. But the scenery is beautiful, the site is magical, and the archaeological places are of great interest. I believe that it is worth it!
We really enjoyed it and we were happy we decided to go, but it was a bit far like other answers it really depends on how long you have and if you want to commit to that long of a commute to get there. There was a decent museum there as well. We booked with one if the day trip companies and really enjoyed our guide I also think this helped get more out of the trip.
Yes, go! If you enjoy archeology and scenic areas, I think it's worth it - it was one of the highlights of my trip. I spent 2 full days in Athens and was satisfied - I had enough time to see the museums and neighborhoods I wanted, and then I drove up to Delphi (most the drive is really easy on a wide freeway and in the morning took just over 2 hours). It had absolutely gorgeous views from the top of the site; driving in/out was very scenic. I loved walking throughout the site, as well as enjoyed the adjoining museum. There are also plenty of day trips with tour companies you can schedule if you don't want to drive yourself. You could definitely be back in Athens well before dinner and still have the evening to enjoy in town.
I would say see how much you're loving Athens when you're there, and play it by ear if you want to rent a car or join a tour one day to see Delphi.
Since you have just 3 days in Athens, I'll go ahead and say no. According to Google maps it's a 2hour drive there but it can easily get longer. Also apart from the archaeological site there isn't much else to see around! It's better to see more of Athens! And if you do fancy a half day trip may I suggest Sounio which is closer and has stunning views (and still...it is half day)
Definitely, if you have the time, the trip to Delphi is worth the trip. It is interesting, you get to see some of the country side and is a little break from Athens.