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, you need so much ore so your second base should be dedicated to that. Find a good ore site, and employ a bunch of Tombats to mine for you (easy to find, 2 in mining and they don't need sleep). Eventually you should head to the western desert (Where Anubis is) to catch a bunch of Digtoise (3 in mining) to replace the Tombats.

An there are plenty of ore sites on the map, so I judged my locations harshly: plenty of ore, easy to defend from raids, and bonus points if near a skill berry tree that is not already near a fast travel.

The reason for this is that on my server I like to fast travel around to every skill berry tree at the end of the day and there are only a few trees that are not a quick trip away, so you can use this base to add another berry tree to your fast travel circuit.