It will be my first time in all of those places, I have about a week and a half to two weeks for them, and yes, I will be checking out major tourist attracts like the Alhambra, El Azacar, etc. How long would you plan to be in each place with my limit of 14 days? I want to see the major sights and get an initial feel for the culture of the different cities, and then plan an in-depth return visit to places I'd like to explore further. I understand this isn't really enough time to fully visit a place, but it's what is feasible right now

While a week and a half might be pushing it for those 4 cities, having up to two weeks makes your plan a breeze. Granada
is well-worth two or three days. Be sure to reserve your Alhambra ticket well in advance of your trip as those who just turn up in Granada sometimes can't gain admission on the fly. The Albaicin neighborhood is another highlight. Seville, the capital of Andalusia, can easily fill at least four days. The city is packed with attractions and difficult to leave, even when you have to. Córdoba is worth a couple days. You also could remain in Seville and daytrip to Córdoba since it can be reached in 45 minutes by train from Seville. Both Seville and Córdoba are on the same high-speed AVE train line going to Madrid in 2.5 hours. Massive Malaga has a ton of attractions and its beaches to soak up the remainder of the time you have- four or five days.
Personal opinions:
- Malaga 1 or 2 days
- Cordoba 2 days
- Seville 3 or 4 days
- Granada (Grenada is somewhere else!) 2 or 3 days
This means full days, so travelling time is on top.
In 2 weeks you have time for other places.
I'd go with 3 full days each in Seville and Granada,and 2 days each in the other two.That makes 10.
If you add travel days that is your 2 weeks....

Thanks, all. It seems everyone can agree Seville certainly requires adequate time to appreciate!

Have a look at what you want to see in each city and then work it out from that. Everyone has their own preferences for me I prefer Malaga and Granada so I would spend longer in those. For others it is Seville. You don't say the time of year that could things a bit as well. The other way is don't book anything, head to the first city and take it from there.

We flew in and out of Malaga earlier in the year (March) and spent two nights in Malaga (first because the plane touched down late), four nights in Seville, two nights in Cordoba, two in Granada and then back to Malaga for one night before the flight home.
Tickets for Alhambra visit were booked back in January - we collected our tickets around 9am at Alhambra's ticket office and the Sold Out sign was already up.
We used buses to get around (booked via www.alsa.es - used PayPal to make bookings as we don't have Spanish bank cards). Booked in advance to get the best prices, but that did reduce our flexibility a bit.
Already planning a return visit!
It works nicely to describe things in nights, rather than days, because it then covers travel between places. So three nights in each place is about right - although disclosure, I've not been to Cordoba. So twelve nights fits into your envisaged timeframe.
I understand this isn't really enough time to fully visit a place, but it's what is feasible right now
Considering that it is part of your broader plan to return at a later time, you are really worrying about nothing. You do not even have to try to see everything, or to distribute your time NOW in a way that is proportional to what is possible. Basically, anything and everything is feasible. You have to decide what you want. It's a personal choice.
I typically start with #5's first sentence. It is easy to give yourself one or two priorities. With that, and with your other stated interest to try to get a sense of the overall ambiance of a location (not merely the tourist attraction 'musts'), you are in the best position to judge for yourself how much time you want to give yourself during a first trip reconnaissance. The notion that there is somehow a best way is simply fallacious. A person could do an information gathering trip on one week, with one overnight stop in each town/city.
With any amount of time you have, divide days by number of locations for an even distribution. If you want to tweak this with a more detailed consideration of how you want to spend your time in any one location, by all means do so.
For example, I'd use Malaga as an arrive/depart airport base, give 4 days (including travel day) to each of the other destinations and left over days in Malaga. I'd go in off-season because I have little interest in beaches anyway. And I'd still give myself the option to add or subtract a day to any of the destinations.
One intangible is that 'feel' for a place, and the degree to which you like to wander or just be somewhere (in contrast to hitting the tourist sites). Sometimes I can tell what appeals to me, and what I want more of, even while I am somewhere. At other times it may take a while for all my impressions to sink in. I need to have been at each of several destinations before I can adequately compare them on that elusive 'feel'. Any subsequent trip will then be better informed by my own experience at the destinations.
So why not treat the trip for what it is, an initial exploration?
A few years ago I discovered by chance a great travel planning tool that draws up tourist itineraries in each city.
Is the website visitacity.com.
On the site you'll find scripts to the major cities of the world allocated in maps , with estimated time of the visit, hours of operation and time and distance of the route between sites. You can also customize the scripts by adding and removing sites, by adding your hotel, restaurants and everything else you want to do in each city. I have used this tool and my travel itineraries have improved greatly.