Welcome to Gateon Port, the main port town of Orre. As soon as you enter, you will be attacked by Thug Zook's Shadow Zangoose. However, a certain person will step in and battle for you, so don't worry about it. After the scene, head left to reach a short row of houses. You will meet Emily and Acri, then enter the parts shop next to you. The shop owner isn't here right now, but talk to the sailor there; he'll give you your choice of Eevee evolution item! Pick one and use it if you like, then head back outside. Go to the bridges and talk to the guy with the red hat. Now go back to the store and claim the machine part from Perr. After exploring the town, head back to the lab and hand over the machine part to your mother.
Now that you've done that you can go to Agate Village. Head there when you're ready.