Where do most old people die hospitals, home, senior care places?

In nursing homes and hospitals 

This is simply impossible to know.

People just die wherever they happen to be when their time is up. Dying isn't something that we can plan down to the last detail.  Where we die, in what manner we die etc. can never be planned. With all the planning in the world we could still meet a very sticky, unexpected and untimely death.  All that we have to do is accept that that is how things are and don't expect our loved ones to have an easy time disposing of us.  When our funeral will be will all depend on the circumstances and timing of our death.  Plans are good to have but we cannot assume that they'll be carried out to the letter. Sometimes the law has to intervene as in a murder, suicide, certain kinds of accidents etc.

Far more people seem to live out their last days in care homes these days but some might be hospitalised during their last days whilst others might have been taken home to their children's home for a short stay and could die there.  We should not be concerned about this as we will not be the ones doing the arranging of things.

This will vary all the time.  People die when their time is up. The venue will not play a large part in the death.  Some people go on holiday in old age so some will die whilst away from home, possibly even in a different country from their home.

How the hell should I know that?

I'm guessing hospitals. 

I plan to live forever. So far, so good

probably in all 3 places

Yes, yes and yes.

Answers vary by geographical location, culture and economics.   In some countries/cultures, people do not farm out their ill/elderly to care places even if they have the money to do so.