10 nights in Spain

I'd probably drop one stop and spend more time in Seville and Barcelona. I'd drop Nerje and make sure you see the Mezquita in Cordoba. That could be done as a stop on the trip to Seville; I think there is luggage storage at the train station but obviously that would be important to know. You need two nights in Granada to get one full day for the Alhambra in Granada.
https://janettravels.wordpress.com/2013/09/27/the-mezquita-at-least-the-catholics-had-the-good-sense-not-to-destroy-it-when-they-desecrated-it/
Or if you add a night to Seville, you could do a day trip from there.
The Mezquita only takes a couple of hours but it really was the most wonderful thing we saw in 2.5 weeks in Spain a couple of years ago. Be sure to get your Alhambra tickets well in advance. The Alcazar in Seville is almost as good as the Alhambra so another option if Nerje is a big deal to you would be to drop Granada.

Your first option works best, unless you particularly want to include Malaga.
Why no time for Madrid & Toledo ? You could work them in to an intense 11 day trip if you are just wanting to see the big sights.

Day 1 - Arrive Madrid - 3 nights
Day 2 - Madrid (Royal Palace + Prado)
Day 3 - Toledo
Day 4 - Train to Cordoba (Mezquita) then to Sevilla - 2 nights
Day 5 - Sevilla (Real Alcazar + Cathedral)
Day 6 - Train to Granada - 2 nights
Day 7 - Granada (Alhambra)
Day 8 - Fly to Barcelona - 3 nights
Day 9 - Barcelona
Day 10 - Barcelona
Day 11 - Depart Barcelona

I think your itinerary is fine for a busy one. I've never been to Nerja, so I can't commend on skipping it in favor of more time in other places. I think this is a matter of what kind of trip you want to have - a tasting platter of more places, or more in-depth at fewer places?

See if you can fly into Seville (SVQ), which, even with the plane change, will be easier than flying into Madrid and getting to Atocha station to get to the train. Among other things, if you get this on one ticket, you will be "protected" if your arriving flight is late (they'll put you on the next available flight at no charge). If you take a separate train, you either have to risk missing your discount advance purchase train, or buy a last minute ticket on arrival, which won't be cheap.

Or possibly (?) fly into Malaga, car from there to Nerja to Granada. Drop car. Train (3.25 hours) to Seville. Then early morning train (45 min) to Cordoba for a few hours and on to Barcelona by train (4.5 hours), last train leaves at 5 pm, so you get to Barcelona in time for dinner. MIght be more flight options into Malaga if Sevilla doesn't work out?

Madrid's Atocha Station probably isn't the largest in Europe, but it's plenty big, and it's the most confusing one I've seen. If you're flying in from the US or Canada, you'll probably be fuzzy-brained that first day. Be sure you have plenty of time to do whatever you need to do at the station. At a minimum, you'll need to get directions to the correct platform, and sometimes there's a quick scan of suitcases. If you don't want to buy your ticket in advance because of schedule uncertainty, you'll have to deal either with the ticket machines (you may have to pay with small bills rather than with a credit card) or the take-a-number queue at the ticket office. Alternatively, you can search out the El Corte Ingles ticket agency somewhere in the building (modest extra cost).

Another potential complication is that, if you decide to wait to buy the train ticket till after you arrive (giving up the possibility of getting a low-cost, non-refundable ticket), you may find that a lot of the trains are sold out.

I have no idea how big a buffer you'd need between your scheduled flight arrival time at Barajas and the train departure time from Atocha if your wanted to buy a Madrid-Seville ticket in advance.

You buy your tickets to Seville at the Renfe station at the airport where you also get the free tickets to the Madrid train station (Atocha). At the airport they will sell you tickets for the next available train to Seville, taking into account what time you will get to Atocha and the time needed to get through the station. If memory serves, it isn't very far from the cercanias train to the high-speed Seville train and there are signs and people you can ask.

If you are 60+, you can buy the 'gold card' at the airport and get an immediate discount on the train tickets.

Forgot about the rail station at Barajas. I'm the clasic case of brain-dead after a trans-Atlantic flight.

The Tarjeta Dorada is very valuable if you're over 60 and haven't pre-purchased all your train tickets. Just have your passport handy when you want to buy it. So far no one has asked to see anything other than the T.D. when I'm buying a ticket, nor have the ticket inspectors on the train asked to see the T.D.

Just yesterday I was given a senior discount (perhaps 25%) on an inter-city bus ticket from Trujillo to Caceres. I believe the bus company was Avanza. I think it's a new policy.

I obviously look my age, because many museum personnel have asked whether I qualify for the senior/pensioner discount. The age threshold is 65, and I'm not there yet, but I've found that I sometimes still get the discount (which can be substantial) if I tell them I'm retired ("Soy una pensionista"). Mostly no one seems to care that I'm not an EU citizen.

In March, I got the TD using my driver's license, so any photo ID with proof of age is acceptable. In Spain, unlike most of Europe, the 65+ discounts are for everyone, except for a few sights where only Spaniards are eligible.

Thanks for the suggestions. I had to step away from planning for a bit. Still don't have tickets, but have decided against flying into Madrid and dealing with trains right away. Still sticking with 4 stops - Barcelona, Seville, Nerje, Granada. I want to keep Nerje on the list, as I think it would be nice to spend a couple nights in a small beach town after the busy time in Barcelona and Seville. Granada is only 1 hour drive from Nerje, so I was thinking we could get there early and spend our day and night there and fly home from Granada. My concern is also about the weather in Seville and Granada in September. I've been reading that the temps can be over 100. Is that usually the case in early September?

A quick check online yielded an average high of 90 F for August and 82 F for September, so I'd guess that early-September daily high temps would average in the upper 80s. Temps over 100 would not be usual, but I'd expect it to be very hot.

Sevilla may offer better connections than Granada for your homeward departure

Day 1 - Arrive Barcelona - 3 nights
Day 2 - Barcelona
Day 3 - Barcelona
Day 4 - Fly to Granada - 2 nights
Day 5 - Granada (Alhambra)
Day 6 - Bus to Nerja - 2 nights
Day 7 - Nerja
Day 8 - Bus/Train to Sevilla - 3 nights
Day 9 - Sevilla (Real Alcazar + Cathedral)
Day 10 - Day trip by train to Cordoba (Mezquita)
Day 11 - Depart Sevilla

An attractive option if you are open to driving would be to pick up a car on Day 6 when leaving Granada. You could then travel to Sevilla on Day 8 with a possible stop in Ronda. Return the car in Sevilla.

I looked at wunderground.com where you can get historical weather data. For Sevilla, Sept 1-15, over the last 5 years, highs have been in the mid-30's or lower everyday, with only a very few days going over 35 and none as high as 40.

Thank you David, that looks like the perfect itinerary for us. At the moment best flights I can find are either into Barcela out of Granada OR into Seville and out of Barcelona. So maybe it would make most sense to do your suggestion, but reversed. Start in Seville - Nerje - Granada - Barcelona. As for the heat, I guess we will have to just deal with it, as the first two weeks of September is when we can go.

There is nothing to stop you from reversing the Granada-Sevilla portion ...
Barcelona - 3 nights
Sevilla - 3 nights
Nerja - 2 nights
Granada - 2 nights

My philosophy with the heat is that you need to experience the heat in Andalusia to gain a fuller understanding and greater appreciation of the country. So much of the lifestyle/architecture/cuisine is climate induced. Enjoy.

I day tripped to Nerja last October and wished that we had stayed the night,the Balcony of Europe gave great views of the sea with many restaurants to enjoy the view,Granada for us was The Alhambra and not much else,Seville is quintesential Spain,beautiful city.Barcelona is a great city,be sure to spend time on the waterfront,not to mention Sagrada Familia and the other awsome sights.
Mike