My 19 yr old nephew stayed alone in a hostel in London that was clean, safe, and nice neighborhood( some are way too rowdy and areas a bit seedy).It was called the Aster Hyde Court. He was in a 6 bedded room, but we booked last minute, other wise I think he could have gotten as smaller room( private).
I have heard alot of good comments about the MJE hostel in Paris,, even met an Australian girl who was staying there and she was happy with it . A girl at my work who was just 18 stayed at the St Christophers Hostel in Paris, clean etc.. but it is not as central as some,, but she did like it.
In Rome,, google for convents that rent out rooms( yes, seriously,, safe, clean and central,, cheap too, most often no a/c so consider carefully about that.. a/c in Rome in July and August is pretty important)
Amsterdam,, there is a Christian youth hostel I saw once,, safe, clean, great location, but,, I forget the name,, yikes,, maybe google for it.. the reviews I read were very good( you do not have to be christian ,, just no boozing( in the hostel I mean) or drugs,, which considering your brother is only 16 is not a bad idea)