Suggest purchase of open jaw airfare to assist w logistics to max your time. Open jaw allows you to fly into one airport and out of another.
Does two weeks include your travel time to from usa?
My recommendation is (due to individual taste):
Fly to barcelona, rent an apt (saves money, more space and a kitchen) and stay four days. There is a huge menu of opportunity including beach, montserrat (hiking), great parks for picnics and people watching and you might even choose to visit some of the well known tourist sites. Subway is fantastic and bike rental on the streets at your fingertips.
Now for the next two destinations keep in mind the potential of hot, hot hot is rising (pun intended) so you should slow down and beat the heat by being Spaniard and taking siestas. The good news is you can also stay up late like the spanish and make up for siesta time. Stay well hydrated.
Fly to Granada and spend four days, also rent an apt (make sure it has an a/c). Alhambra is the ultimate mixture of walking amidst fascinating history. The sierra nevada mountains are at your doorstep and offer excellent hiking and mountain biking experiences. An hour away is nerja offering a beach experience. The point is for the items you listed and the relaxed style of travel you mentioned Granada offers alot. Sit down order a drink and get a free tapa then watch humanity flow by. If you were going this year i would say keep an eye out for our daughter as she is spending the summer in granada.
From granada i would take the bus/train to seville and spend the rest of your trip there. Again do the apt thing. From seville you can take a day trip to ronda which offers great hiking into a deep gorge filled w history. You can also daytrip to cordoba via train and there is ample to do in seville.
Fly home from seville.
Sacrilege! I did not recommend madrid or toledo or .........
To me Madrid is more about visiting museums amdist a small old tourist town (trust me I am going to be abused for making that statement (fire away Nancy in Bloomington ;). ) and madrid is the third largest city in europe. Again, using the info you provided, I have provided an itinerary covering a large geographical area of spain and providing three distinct flavors of spain. Plus this is a trip designed to minimize travel stress and max enjoyment as you defined it.
Okay, time for me to get out the kevlar...... Is there a Retired Marine ready ro come to my defense?