Q: When is it recommended to eat on Eid day?
A: On Eid al-Fitr it is recommended to eat an odd number of dates before going out to prayer.
On Eid al-Adha it is recommended for those slaughtering an animal to delay eating until after prayer so that the first thing eaten is the Udhiyyah/Qurbani. It is recommended to eat the liver because its the quickest thing to prepare and digest.
If there is no slaughter being performed, one can choose to eat before prayer or after.
Source: Kashshaf al-Qina'