Learn English – you from? Singular or plural

Both present perfect have lived and present perfect continuous have been living are grammatically correct and natural in this context, and there is no significant difference in meaning because for 25 years nails the duration.

If you are indeed thinking of making a change, using present perfect continuous in your sentence would indicate (very gently) this intent.

In other contexts where you are specifying a long time, the meaning may have a slight effect on the choice of tense: the present perfect tends to focus on the time that has gone by, whereas present perfect continuous is more progressive, focussing on the situation at the end of that time, for example:

I have lived in this town for 25 years and I have seen a lot of changes over that time - focus is on the 25 years
I have been living in this town for 25 years and I still don't know where the police station is! - focus is on the situation now.

If the time interval is not specified or different, present perfect would more likely be used for longer, permanent arrangements and present perfect continuous for shorter, temporary arrangements:

I have worked here for 25 years
I have been staying with my brother until I can find a place of my own.

The idiomatic expression is to put someone up:

to provide someone with a place to stay temporarily:

As in

• Sally is putting me up for the weekend.

“Where are you put up” is an uncommon usage of the above expression

“Where are you staying?”, would be a more correct and common way to ask.

from to stay:

to live or be in a place for a short time as a visitor:

as in:

• I stayed in Montreal for two weeks then flew home.
• They said they'd stay at/in a hotel.