Hi I can see its been 3 weeks and you've likely made your decision. I and my family (children then 6 and 10) lived in Nairobi for 4 years, but came back 13+ years ago. When we came back to UK our eldest was 14. I'm guessing lots has changed, but treat this as historic.
I'm guessing you'll be at the UN? ISK is a good choice of school, or was then. You don't want to pick somewhere in a long commute away, as the traffic can be nightmarish in the rains.
Our children had been used to going independently to the park and corner shops before we went to Kenya, and this was a big constraint when we were there. It also depends on your personal attitude to risk, and many (Kenyan) families were far laxer, but we were attached to an embassy, and got very direct security briefings. When my oldest got their first boyfriend and wanted to hang out independently in the mall with them, I set up shop elsewhere in the (large, Village Market) mall for hours, drinking coffee, so I'd be close in case of a security alert. This may seem over alarmist, but 6 months later was the Westgate attack.
We had guards, and escort vehicles to come back at night, and a safe room. It took getting used to, and by the time we left 16 friends had been held at gunpoint, etc. That said, road safety is the biggest risk, and you do adapt, and if you have good security (which you would from UN), and treat guards/staff well, the risks are much reduced.
One of the other things to be aware of is being next to peers who are from multimillionaire families, and attitudes formed then, eg teenagers having drivers at their disposal to get them pizzas at school at lunchtime, conspicious consumption. That said, we found being clear, this isn't how we do things in our family, or, this isn't how it'll be when you're back in Britain, so you're making your bed yourself, worked fine. And as you'd expect there was a broad range of income, we weren't the only ones.
It was a big transition for our children coming back, particularly the then 11 year old. They'd been in a Kenyan British-curriculum school. It has given us all very vivid experiences/world views/sense of comparison/friendships and some amazing holidays, which I'm grateful for in a lifetime, but the challenges aren't to be underestimated. On the other hand you forge deep friendships very fast, and overall, I'm very grateful to have had those 4 years there, as are our children.
Good luck. Hopefully you've found someone who is there now to ask, but do pm me if I can help more, though I'm really conscious how out of date I am.