The Mark of Kings is required before Lord British will raise a character's maximum HP above 550. Therefore, you won't need it for a while, though it doesn't hurt to find it early on. The Mark of Kings is available in multiple locations in five dungeons, and can be easily obtained in a number of ways.
The easiest place to find the Mark of Kings is in the Perinian depths, where it can be found on level 01. It's found almost as easily in that dungeon by taking a ladder from level 02 to level 08. You'll have to deal with tougher monsters there, but you'll find nearby Healing and Curing Fountains, as well as the Mark of Fire.
You can find the Mark of Kings similarly easily in the Mines of Morinia. The entrance ladder leads all the way to level 08, and the walk to the mark isn't very far. Alternately, you can take the direct ladder to level 03 and find it that way, though that path requires you to deal with some gremlins.
The mark is also easily found on level 02 of the Dungeon of Time or Dardin's Pit. It can alternately be found on level 08 of those dungeons or the Dungeon of the Snake, but it's difficult to reach those locations with the limited HP you will have.
The easiest place to find the Mark of Kings is in the Perinian depths, where it can be found on level 01. It's found almost as easily in that dungeon by taking a ladder from level 02 to level 08. You'll have to deal with tougher monsters there, but you'll find nearby Healing and Curing Fountains, as well as the Mark of Fire.
You can find the Mark of Kings similarly easily in the Mines of Morinia. The entrance ladder leads all the way to level 08, and the walk to the mark isn't very far. Alternately, you can take the direct ladder to level 03 and find it that way, though that path requires you to deal with some gremlins.
The mark is also easily found on level 02 of the Dungeon of Time or Dardin's Pit. It can alternately be found on level 08 of those dungeons or the Dungeon of the Snake, but it's difficult to reach those locations with the limited HP you will have.