A base can be built under the altar of the Elder. It can be built deep enough for 2 stories and offers protection from mob events. On my seed map it is between the Swamp and Mountain biomes, very close to both.

https://steamcommunity.com/sharedfiles/filedetails/?id=2817766710
I will build stone walls and an iron gate around the portal to protect it.

https://steamcommunity.com/sharedfiles/filedetails/?id=2817766619
After digging under, before building any permanent structures.