"Mieszkałem", for instance, seems like a bad choice as it means "to live". I didn't 'live' there, I just stayed at a hotel.
Avoid such one to one translation pitfalls. Polish 'Mieszkać' is not the same as English 'to live'. Both 'to live' and 'to stay' can be translated as 'mieszkać' if you're saying about the place which you occupy during your life/stay.
Mieszkam w ładnym domu - I live in a nice house
I stayed in a hotel during my last visit to... - mieszkałem w hotelu podczas mojej ostatnie wizyty w...
However, when you're talking about other aspects of your life (e.g. your social status, lenght etc.) you usually translate 'to live' as 'żyć'
My grandma lived longer than I would be - moja babcia żyła dłużej niż ja będę żyć... (because she lived healthier)
During the war people lived as rats - podczas wojny ludzie żyli jak szczury (whatever that can mean ;-)