Hi there PPP! Your local representative of Segovia speaking here...
I totally agree with the itinerary proposed by David B. Use the extra time instead of Granada (one of my favorite cities) to see Madrid. If you can´t get into the Alhambra (as Sel suggested double check that it is open!!) then that takes a huge chunk of attraction away from Granada (in my opinion). Going to Spain and not seeing either Madrid or Barcelona is kind of like traveling to the Northeast USA and not visiting NYC. Get my drift?
With the extra time in Madrid, definitely plan a
FULL DAY in Toledo. It will be a bit chilly in December, but not nearly as cold as NYC.
Save Segovia for a subsequent trip. Segovia is more than just a day trip and more than just the Aqueduct and Alcazar. It is also La Granja and its gardens in San Ildefonso(former summer palace of the Spanish royalty), it is the Sierra (mountains to hike), the castle of Coca, side trips to El Escorial, Ávila and Valladolid and all the wine and cheese towns in between. Besides, Segovia in December is freezing cold... a dry windy cold (different than the east coast USA). Best to visit in spring or fall when the leaves change.
Believe me, I´m a huge fan of Segovia (heck, I live here now!) but you don´t want to overdo it. Besides, from NYC you can get some dirt cheap fares to Madrid....and seeing as you aren´t even 30 yet, you have plenty of time to fall in love with Spain!!