Question:
Could I have a teenage babysitter watch my children at night including an 11 year old boy if we are in the city
Answer:
Than you for your question.
The fact that you are in the city is not enough to permit the teenager to babysit your 11 year old son, since you are not expected to return home soon.
This doesn’t automatically mean that she can’t babysit for you, as your other children might otherwise prevent the yichud, but that would depend on how many they are, their age and gender.
Best wishes