[susan53]

Present perfect verb forms have three basic uses :

a) To express an event which started in the past and continues until the present moment. With this use there is no difference in meaning between the simple and continuous forms if the event can be seen as either stative or dynamic :
I've lived here for 3 years = I've been living here for 3 years.
just as you could say either I live here now or I'm living here now.
If the event must be seen dynamically, only the continuous can be used, eg :
I've been trying to do this crossword for the last three hours and not * I've tried...etc (just as you would say (I'm trying to do this crossword but it's really difficult, and not I try to etc.


b) a past event (or events) in a time frame which is both past and present. In this case the simple form suggests that the event is complete and finished :
I've read War and Peace this week = ...and have finished it
while the continuous suggests that it is unfinished and ongoing :
I've been reading war and Peace this week = and have reached p. 97


c) A past event with a present result.
In this case the simple form suggests that the event happened once : I've cut my finger!
while the continuous suggests that the action was repeated several times : Someone has been cutting pictures out of this book!


Your example with stay doesn't work though. Firstly, for the context you mention there is no connection with present time. The event is not continuing into the present (explanation a above), the time period is clearly finished, and doesn't continue to the present (as in explanation b)(it's last week not this week, or yesterday not today), and there's no suggestion of a present result. So the sentence would be : How long did you stay in New York.

However, if the person was still at the Hilton Hotel, then the perfect becomes possible (it's now a past to present event). But because the lexical meaning of stay is temporary residence, it must be seen as a dynamic, unfolding event - not as a state. So only the continuous would be used :
- I'm staying at the Hilton Hotel.
- Very posh! How long have you been staying there?