We never left our kids with stranger babaysitters until they were old enough to tell us how it went ( not toddlers! ) . We left them alone in room by 11-13 or so . Old enough to babysit back home means they were old enough to be alone in a room with orders not to leave room . We stay on smaller hotels ususally where strangers can not just wander past the front desk .
I was once on a trip to Europe with one of my kids , (11 yr old daughter ) we were in Paris and I got dreadfully sick . I had to let her go out on her own during day to find something to eat ( sent her down street as we knew there was a bakery nearby) . Scary for me but she did fine .
Another year I took my 13 yr old son and I let him go down street to grab mcdonalds before bed , lol, he did this several times just fine .
A lot depends on you child's maturity .
I wouldn't leave kids iner 10 alone .