Make sure you get treasure T6 - Strange Map. This will unlock the World Map, Dungeon Map, and Town Map for the entire game!
Also, make sure to collect all the Dragon Pearls. You won't be able to use them for a long time yet, but ultimately you will need to collect every single one.
There's no boss in this dungeon, so once you've got all the treasure, head back to Northwest Town. Now that you have the Bandit Key, you can unlock the home on the west side of town and get the treasure - a Leather Shield.
Now go to the Inn and talk to Mizenda. You'll be prompted to add her to your party, but instead of joining you, she asks how Linn in the neighboring town is doing...
Now talk to the guy standing guard at the town entrance, and he'll move away and let you leave. Now, you want Mizenda to join your party, but if you go to her town right now she won't join you, and there'll be nothing to do there anyway. So instead, head south to Temple Town.