After leaving the forest you'll be presented with the Big Map screen, which you should know how to use because you ran the tutorial (right?) As you enter Seaside Town, the music and atmosphere tells you right away that something is wrong. The buildings are burned, and the people are mostly gone.
Near the center of the village you will find a chap who will tell you that everyone has gone south. If you opened all the chests in the room immediately below the cell where you escaped, you will have a letter and this chap will trade you the letter for a badge. Good deal.
The library has a basement, which you will need to enter. In the basement you will meet Rios, the librarian and a Cleric. He will join your team and having a Cleric with you means you can get on the boat waiting at the docks (you can try getting on the boat without Rios but you will not be able to.)
In the small building near the docks you can find some chests with some small items of value.
The shop mostly survived (at least it kept its roof!) the firestorm brought by Tiggy and his summoned monsters. Here it is a good idea to buy all of the new and better equipment for your team (You may need to revisit the shop later as you acquire a new party member.) You can also buy some common items like Cures, Heals, and Elixirs at this shop which has a better price than most (but not all!) shops.
There isn't much more to this town at this point. You'll want to head East as that is where Tiggy went, so talk to the sailor on the dock and he'll let you on his ship if Rios has joined your party. You'll then see the Big Map again where you can select the Eastern Docks as your destination (other locations are blocked, since they aren't reachable by ship.)