This whole event is pretty much finding the eggs. That’s it. You can find them anywhere you want*, but you do need to find your bunny some love in certain locations, so eventually you’ll need to go to the other three egg hunt locations. No sweat.
*Edit: I mean in any of the 4 hunting locations (first town in the starting zones for your factions).
Do yourself a favor and don’t tempt fate: yes, you can buy almost all of the items you’ll need for the achievements, but that just guarantees the next egg you open will have the item you just bought. Seriously. Instead, find and open eggs until you find the dress, pants, and shirt. By then you’ll have enough chocolate eggs found and saved to buy everything else if you haven’t found them by that point.