The "best" underground housing I use is to dig out underneath the Elder altar, which provides a very sizable space to live, and the altar ceiling provides 100% safety as it is completely indestructible. I say 100% safety because in all my playthroughs I have never had a single mob get anywhere close to reaching the underground living space.

I completely dig out all the ground under the altar and then place wood walls and ceiling etc to make it more aesthetically pleasing, also this allows me to recess many of my work stations and storages for a much cleaner living space, and to allow a place for smoke to safely rise up and linger before it dissipates. (since there is no way to actually vent it out through the altar ceiling)

https://steamcommunity.com/sharedfiles/filedetails/?id=2643985164

https://steamcommunity.com/sharedfiles/filedetails/?id=2643985634

https://steamcommunity.com/sharedfiles/filedetails/?id=2643985888

https://steamcommunity.com/sharedfiles/filedetails/?id=2657700955

https://steamcommunity.com/sharedfiles/filedetails/?id=2643986592

https://steamcommunity.com/sharedfiles/filedetails/?id=2643986196

https://steamcommunity.com/sharedfiles/filedetails/?id=2657677489

https://steamcommunity.com/sharedfiles/filedetails/?id=2643986792

I imagine there are other places in the world where it is possible to dig under them and build safe underground areas but this is my go-to place for underground living.