How Alberto chooses to run away doesn't make sense. First he's carrying a suitcase even though he came into Portorosso with no possessions, not even a change of clothes or a suitcase, for that matter. Second, as a sea-monster, his best means of leaving is to jump in to the water which is right by Massimo's house. Instead he's shown walking up the street which the movies shows leads to the hills which makes no sense for someone trying to get out of town quickly and go somewhere else.
Alberto might be carrying the letters he got from Luca in the suitcase, and he would not have wanted to get them wet. The Aragosta sisters, who are also sea monsters, live on the highest part of town by the will. They know Alberto and like him enough to get him ice-cream at the beginning of the short, he could have been heading to their house. Plus, upset as he was, Alberto was hardly acting rational.
The suitcase could also be packed with belongings from the tower on the island he used to live in, which he brought over to Massimo's when he moved in. Regarding him trying to run away on land, he was also planning to do that with Luca in the movie, which implies that he just finds living on the surface more appealing than going back to live in the sea.
Alternatively, on some level, Alberto wanted Massimo to come after him and stop him from leaving, which would be made a lot easier if he just walks away down the road rather than swimming down into the depths where Massimo isn't able to go. It's not unheard of for someone with confidence issues as bad as his to try something like that for attention or sympathy.
He also might've been going to the train station to catch a ride to Genoa, to meet back up with Luca and regroup or something.
Alberto's adoption
With Alberto having been adopted by Massimo, and the short confirming that he now stays in Giulia's tiny bedroom, how do the sleeping arrangements work when Giulia and Luca come back from Genoa every summer? It doesn't seem like Massimo has much room to spare for a second bedroom. Luca may be able to go home and sleep at his parents' every night, but... Is Alberto going to return to sleeping outside in Giulia's hideout the entire summer?
Massimo could always put a second bed in their tiny room for when Giulia comes to visit, Alberto might not mind sleeping outside but his dad would.
