Stay in Madrid city or outside of city

I don't see any advantage to having a car for trips to Toledo and Segovia. Toledo, especially, is one huge historic district that I assume you wouldn't be able to take the car into. I imagine you will need two or more days to see the sights in Madrid, which would mean commuting into the city at least twice. It would be far simpler just to be in the city.

It's very easy to get to Segovia or Toledo from Madrid via public transit, and Madrid is a nice city to get up early in as well as stay up late in. Staying outside of the city and renting a car would be a waste of time and money in my opinion.

There are plenty of hotels or short let apartments near the Atocha train station. That also puts you on the subway/bus lines for when you want to wander Madrid. Museums are close as well as great streets for tapas.

I day tripped to Segovia and stayed two nights in Toledo,lots of history very easy to do from the train station and stay in Madrid.
Mike

Definitely stay in town and take public transit for day trips. (I speak from personal experience having been there in 2001 and again with my wife in 2005). Bus used to be more convenient for Segovia, but check Rick's book or other guidebook for the latest. Train might be better for Toledo but they were working on the train line when I was there last so we took the bus. Madrid itself is wonderful and much underrated. But there is also El Escorial..

I agree with everyone else; stay in town and use public transport for the day trips. While you can drive in parts of the historic center of Toledo, the streets are very, very narrow in spots and there is almost no parking. You'd need to park outside the historic center and walk. On my last trip, and before checking into the hotel, I found some parking by the Bridge of San Martin outside the historic center. I've always had a car when in Toledo, but used the hotel parking garage and walked into the historic center. We also continued on to other places in Spain and weren't going back into Madrid. Same for Segovia; very limited parking. Maximize your time to see things by reducing the travel time between places.

We visited Toledo in 2016. We could walk or take a taxi or walk almost anywhere. The taxi fare for the short trips was so inexpensive that it was kind of embarrassing. We spent three nights in Toledo arriving by train.

We also spent two nights in Segovia. Segovia is also very walkable. We arrived by train and took a taxi from the train station to the hotel.

Thanks for all the great responses! Definitely sounds like staying in the city is the way to go. Can't wait!