I would also like to comment that in Greek we may also want to say:Έμεινα στο σπίτι. where we use the article στο without also defining which is the house we live. We may also say "Έμεινα στην αυλή" when we don't know which is this backyard we are talking about while at the same time we say "Εμεινα σε ξενοδοχείο". We could also have used "Έμεινα στο ξενοδοχείο" as we don't refer to a certain hotel,and this is the hotel where we stay now that we know like our house,"Έμεινα στο σπίτι". But instead,we say "'Εμεινα σε ξενοδοχείο". So,which is the difference? When the other person we speak to,knows which is the place where we live,this hotel or this house, we use στο.When the other person doesn't know about which is,we use σε. For example,when the other knows about the hotel we stay and asks if we stay at this hotel or in our friend's house and we say 'I stayed at the hotel" we say 'Έμεινα στο ξενοδοχείο".But when he dosen't know about the hotel we stayed and asks for the first time we say 'Έμεινα σε ξενοδοχείο". So,we can use also "Έμεινα στο ξενοδοχείο΄" but in a different context. The knowledge the other has about us plays important role while in different languages maybe sometimes the use "Έμεινα στο ξενοδοχείο΄΄ in all cases.

Έμεινα στο ξενοδοχείο ==> I stayed at the hotel (at a specific one, as you said) Έμεινα σε ξενοδοχείο ==> I stayed at a hotel (generally, without referring to a specific hotel) So in Greek both sentences are used, having exactly the same difference as between 'the hotel' and 'a hotel' in English. Your last sentence is also correct. I would prefer: Έμεινα στο ξενοδοχείο Χίλτον (=I stayed at the Hilton hotel) hope it helped :)