Enric is right. In 10-12 days, choose two of the following three:
Madrid and around (Toldeo, Segovia, etc)
Barcelona and around (Girona, Sitges, etc)
Andalucia (Seville, Granada, Cordoba).
While these are the most common destinations for a first trip to Spain, if you're drawn somewhere else, that's fine too. Just realize you will then have to drop one of the other areas.
Spain is a larger country than it seems at first, and getting from place to place quickly can be easy or hard, depending on which places you're trying to connect. Do investigate transit links before making any firm commitments. And be open - depending on what you're trying to connect, it may be best by train, bus, domestic flight, or car.
Have you already booked flights from the US (assuming that's where you're coming from)? If not, do look into "open jaw" (multi city) flights - say, into Granada and out of Barcelona. To find these flights, use the "multi city" or "multiple destinations" function of Kayak, Google Flights, Iberia, etc. On a short trip, these kinds of flights can save a lot of time and money in not backtracking, so they're worth the potential "extra cost" up front (and there may not be any compared to a simple roundtrip).
On the other hand, if you already have booked flights, let us know what they are.
How temperature sensitive are you? If you don't mind high heat, you'll be fine in the places you listed. If you do, you'll want to check carefully before planning. Unfortunately, I can't get my usual website (Wunderground) to work right now, but try to find actual historical temperatures for your travel dates in 2017, 2016, etc. This is much more useful than "average" temperatures.