Lenore1

We will be arriving in Madrid Airport at 10:40am and departing at 4:20pm. Does that give us enough time to go into Madrid? If yes, how would you suggest we spend our time there? We have never been to Madrid before. How long does it take to get into the city center and what means of transportation do you recommend to and from the airport?

Thanks in advance for your advice.

danon

if you take in account the time you need get off the plane, and the time you before the departure, you have about 4 hours.
I think it takes about 40 -45 minutes to get to Madrid by public transit; by taxi: less ,but depends on the traffic.
You may wish to take a taxi to the Palace to see it from the outside, there is a lovely park between the Palace and the Opera and some elegant cafes, then walk to Plaza Mayor ( about 10 minutes away), and taxi back to the airport.
The cost for taxi one way is about 25 euros.
Madrid is a very large city ; by taking a taxi, you might at least see a bit of it.

car

It is just about enough time to go and come back spending 3 to 4 hours in town at lunch time.
So relatively good traffic conditions.
I suggest you take a walking tour around the old center, Plaza Mayor,
Royal palace, Plaza de la Opera.
And lunch in any of the hundreds of places you will see in your tour.
Taxi in and taxi out should be convinient, cost around 30€ each way.