Madrid hotel near airport or not

If the flight is a good price, fine. (Check the luggage rules.) We took the train, AFAIR. Because the Madrid metro goes to the airport (long trip), I would stay at a hotel that connects well with that line. However, if your international flight is at 2PM or earlier, I wouldn't bother. You don't say for sure that you will have already visited Madrid, a major city of the world.

We enjoyed our stay at the NH Barajas Hotel the night before our flight home this past October.

{Since we were staying in Toledo, I felt more comfortable staying close to the airport, rather than having to stress about getting up super early to travel to the airport}

I don't recall if we paid extra for the buffet breakfast, but it was certainly worth it.
The hotel was clean, comfortable & it offers a courtesy shuttle to/from the airport.
We actually arrived to Terminal 4 via the Cercanias (C-1 line) train from Madrid (travel time 25 minutes from Atocha)
I notified the hotel upon our arrival to T-4, & the shuttle van took us to the hotel, & then... The following morning, it took us back to the airport!

Depending on what time you arrive to Madrid, you can take the shuttle to the hotel, leave your luggage, then take the Metro to the city center. The hotel staff are very helpful & they will tell you where the closest Metro stop is, etc...

Enjoy your Spain tour!

Tim makes a good point here:

If the flight is a good price, fine. (Check the luggage rules.) We
took the train

We also took the AVE train from Sevilla back to Madrid. Travel time is about 2.5 hours.
You may want to check train schedules here: http://www.renfe.com
Just make sure you choose these trains station from the drop down menu:

• Sevilla-Santa Justa
• Madrid-Puerta De Atocha

Make sure you pack a light rain jacket as we encountered a couple of rainy days in Sevilla & Toledo.
We also experienced warmer weather (mid 80's to high 90's in early to mid October) during our visit to Andalucía (Granada, Córdoba & Sevilla), so you may want to pack a couple of skirts or dresses.
I actually prefer packing skirts, over dresses, because I can wear the skirt(s) more than once with different tops :-)

You may want to check the weather, as your date of departure approaches, instead of solely relying on what is written here on this website: https://www.ricksteves.com/tours/spain-portugal/spain

I just checked the itinerary for the 'Best of Spain' tour, & it's really too bad that you will be skipping Córdoba.

Another option, if you think you will be up to it, is to visit Córdoba on your way to Madrid via AVE train.
You could leave your luggage at the bus station (across the street from the train station), then take a taxi to the historic center
& visit the amazing Mezquita!

Enjoy!

The airport is close enough to downtown Madrid that you can easily catch a taxi or ever a train to the airport.

The express bus between the airport and Atocha station is the best way to get between central Madrid and Barajas airport -- it stops just twice, runs often and all the time, and has urban-style seating, unlike the Cars Air France from CDG to Paris (which I also like).
http://www.esmadrid.com/en/airport-express
If you need overnight lodging in Madrid, there are a lot of business-class hotel choices along Atocha, just past the wide roundabout beyond the train station, on the other side of the building from the bus stop.

Avirosemail is right. The Airport Express is the best way into central Madrid. It only costs 5 euros and stops at Cibeles and Atocha. The trip takes about 25 minutes. Either area puts you very close to lots to see and do. If you want to stay near the airport, I can personally recommend the Hotel Nuevo Boston. They have an hourly shuttle to the airport for your flight out the next day.,