Dragon Quest/Northwest Alefgard
Traveling to the northwest from Tantagel you will find a dungeon and the town of Garinham. Garinham brings a new shop and new weapons and armor, but there is nothing else you can do in this area until you are much higher level.
Enemies that you will encounter here:
Beyond the west bridge, you may also encounter:
Do not cross any bridges until you are stronger. Every time you cross a new bridge be prepared to face stronger enemies.
Far to the north and west of Tantegel Castle lies the ancient town of Garinham. Many rumors and legends surround this place, once the home of the great wizard named Garin. It is said that hidden in the shadows of the town is Garin's grave, and that a "Silver Harp" is buried there too. No one knows if this legend is true, but you should explore everywhere, even in the shadows. The secret may lie behind the closed door, but even getting in may be difficult. From the citizens of Garinham, you will learn more about the disappearance of the Princess.
Of particular note, you should make sure to grab the Chain Mail here, and eventually the Iron Shield, as they are not available in any town other than the last one.
Erdrick's Cave edit
This cave is the first most heroes encounter. Unlike the other caves, it has no enemies within. Be sure to light a torch, or use the radiant spell (learned at level 9) to make winding your way through the dungeon easier. Make your way to the lower level to find a very special message left here for you by your legendary ancestor; there's nothing else of value within this dungeon.
If you do not have either a torch or the radiant spell, under no circumstance should you proceed further into underground caves. In the larger caves, it is quite easy to get lost, even if you are looking at the map, and possible to enter a situation where not even monsters within the dungeon can kill you to warp you back to the castle, especially this one with no monster encounters.