In case you are on a budget, or just want to get away from the restaurants and have a relaxing meal away from the crowds in Delphi, here are some good suggestions:

There are some benches on the pedestrial way from museum towards Athens, and plenty of opportunities to seat down around Kastalia fountain. This is a popular walk among tourists and locals alike. During evenings when crowds have gone, it is a great place to enjoy the views and have a dinner. Even after dark, it is safe and easy to walk back into town from there. No more than 30 minutes walk.

But here are some other spots for pique-nique:

A beautiful spot that people tend to ignore in Delphi, it's the Angelos & Eva Sikelianos Museum. It is located North East of modern Delphi, North West of Delphi museum and  South West of Delphi Stadium. It is accesible only through modern Delphi. Entering Delphi from Athens direction,follow the upper main road till the junction and turn right (opposite taverna Vacchos) Then turn right again.  There,it is the main church of Delphi, called Agios Nikolaos, and the square you see is called "Lekaria".

There is a nice festival with traditional live music taking place there every Greek Easter Sunday, on the PM hours. Anyway, keep driving/walking, till you find the local cemetery. There is space to park your car. The building that is located opposite the cemetry and slightly reminds a castle, is the A&E Sikelianos museum, and if it's open, worths a sort visit.

Outside the museum there are plenty of benches where you can stop, relax, have a meal and enjoy the views. Views from this spot towards Iteal Gulf are great. It takes no more than 5 minutes to drive there, and maybe 15-20 minutes to walk there from modern Delphi's main road. If you want, you can keep walking following the road uphill. If you go left, you enter the higher street of modern Delphi.If you go right, you will find your self in front of a closed gate . From this gate there is a path that leads to the ancient stadium, but it is open only in very special occasion,usually on summer evenings when there is a performance taking place  in the stadium.  On the way to this gate, there are lots of almond trees on each side of the road, and pine trees near/around the gates.

It a very beautiful area to be, especially if you are visiting on February/March, when almond trees are in blossom (small white.pink flowers-great!). So you may choose to stop somewhere there to get some photos and have a quick meal.

An other really great spot for pique-niques is the Pavillion (also known as Touristiko Periptero). Exit Delphi towards Amfissa/Itea. Keep driving/walking till you see  a basketball/volleyball/tennis court on the left. Turn left there. Keep going till the end of the road. There is space to park your car.

In front of you there are a couple of steps that lead on some railed remainings of old church (nothing more than a couple of rocks) and a couple of bunches and a "rock plateau" on the right. You are on the edge of a cliff, so be cautious,especially if you have kids with you, it's advisable to hold their hands, as no railing to protect you from a fall!

You have one of the most magnificent views towards the valley, and all to your selves! Plenty of almond trees,pine trees and other plantation around. When you reached this place, you may have notice a gate and an old building on the left. Quite possibly you can enter the gates and go down some steps till you see it. That's the "Pavillion".

It is owned by GTO, and was running as a cafe/restaurant till about 10-15 years ago. For reasons that are not to be discussed here, it is no more on use, and some people started vandalising it and taking stuff away. If you have children, maybe it's safer to go till what was the restaurants "court yard" and take your meal there. There are railings, but keep always an eye as are not maintened for a long time. Great views and surroundings there too. You need 5 minutes driving or 30-40 minutes walking to get here.

Other Options if you have kids:

Opposite the courts there is a small "platau" among tall Cypress and pine trees. There is also one of these "boxes" that hold a candle in them, and some small rock formations around it to have a seat. Plenty of shade to have a snack, and then your kids can go on the courts (gates are not locked).

If your kids are younger,exiting Delphi towards Amfissa/Itea, on the right, and before you reach the courts, it is a playground. There are swings and the like for the kids, and plenty of benches. A car park is next to it, mostly used from large coaches, but location is very quiet, especially during evenings.