Re: time and money
You can take the Cercanias local train from Barajas airport T4 to Chamartin...journey time around 12 minutes:
Train times & details Madrid>Segovia in English here:
The fastest trains take less than 30 minutes.
I can't recommend a specific hotel (I stayed near Atocha) but whilst you are waiting for members' suggestions have a look at the reliable www.booking.com where you can refine your search by area. The site lists 19 hotels in and around Charmartin.
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