I wouldn't rule it out completely, but only if you could persuade your nanny to learn to drive.
We live in a city, and there are lots of good schools around us, but we chose to send our dc to a school which has a philosophy similar to Montessori. It was a big decision as I am effectively now a taxi driver, but it was the right choice for us. There are days when it is a real pain, yesterday I took the 3 dc to school, left home at 8.20 traffic was bad due to rain, not home until 10, 11.30 got a call from schoolthat ds1 was sick, went for him home at 12.30, then had to leave home again at 2 to collect ds2 and dd. Home at 3.15, exhausted. BUT, I don't moan about it because I knew it would be like that.
The children at our school come form a big catchment area, very few children live within walking distance, so playdates are scattered all over the place.
My guess that your Montessori would be similar, people choose schools like that because of their philosophy rather that the fact that they are local and convenient.
So, I would really work hard on getting your nanny to learn to drive and send your dc to the school you really want.