Here is a collection of the best locations I found when searching for my second base plus any that are shared with me in the comments.
Having a dedicated ore base is essential for reasonable progression in the tech tree, but there are plenty of ore spots on the map, so I judged my locations harshly: plenty of ore, easy to defend from raids, and bonus points if near a dungeon and close to a skill berry tree that is not already near a fast travel.
I have left off locations with extreme temperatures for now.
Location 1: Waterfall Cliffside
309, -36
Pros:
Very Protected, most raids spawn below the cliff
Skill Berry Tree at the bottom of the cliff
Easy access to the Jormuntide Boss
Good start for northern exploration
Cons:
Limited build area
Location 2: Desert Overlook
-35, -167
Pros:
Mostly Protected
Skill Berry Tree is almost inside the base
Easy access to the desert and the Anubis boss
Can collect sulfur from nearby desert
Nearby Caged Pal for easy collection
Base is centrally located for further exploration
Cons:
No scenic waterfalls
