PatriotBrewer...
...what are the legal grounds
if you end up having to dispatch a criminal in self defense?
Exactly.
I'm not a lawyer, nor do I play one on the internet, and we all understand that laws can and do vary from state to state, but with that caveat...
Assuming that a hotel posted a 30.06 sign or whatever the equivalent is in your state, and further assuming that you have found yourself with a legal reason to use that gun while inside your room (where, since you set the rules [within reason] inside the room, I don't think the 30.06 sign will have any bearing), the question will become how did that gun get into the room in the first place?
I don't think it matters whether you asked about gun policy, or if you kept your gun fully concealed until inside your room. The point being: You violated the law by carrying your gun into a place who's owners had legally posted that they wanted a weapons-free hotel.
I will assume that most prosecutors would look at a legal shooting in an illegal location as something that they could use their discretion to overlook, but occassionally, you're going to run into a prosecutor named "Nifong".
In my view, the smart thing to do is not to just sneak your gun into your room regardless of the hotel's policy, but rather to turn around and find another hotel. Let the manager know why you're leaving.