It's not a new idea, it has been done and done well!
Some underground housing makes it seem like you wouldn't even be able to notice much difference being underground and all.
Well, that depends on a few things, mainly the location for several reasons. The main reason location has to be taken into consideration is because you want to be able to excavate land without hitting any old waterworks or previous works that may be included in a city infrastructure. However, if you live in a more rural, less built-up area or better yet a forest then it starts to become more feasible.
So if you can find the location you then have a big job ahead of you if you are wanting to construct your underground home. The biggest part of the job, in my opinion, will be the excavation of earth. Although how you make an underground fortress can be different I would lean towards starting with a concrete foundation, would then cinderblock & brick it then proceed to bury it.
I would definitely think about doing it underground if I were going to build a home.
I think hands down you would be more secure in general underground and not just in a nuclear attack!
Would You Live Underground?