Getting around, Madrid
The suburban trains are included in the tourist travel passes. The suburban trains are a quick way to navigate between the various train stations (or get to one if you are near their route). Google maps, when providing directions via public transportation, does not seem to include them as an option.
The streets in the centre of Madrid are much like a maze and it is easier if you stick to the main roads such as the Gran Via or those that interchange with it. The inner city speed limit is 50km.
Since we were going to tour the south of Spain, we had a car, but we parked it when we were in Madrid and didn't really need it. We walked everywhere.