February and March in Spain

I'm guessing you don't mean literally the southern coast, but rather Andalucia. I suggest picking up a book that covers Andalucía comprehensively along with Rick's guidebook for Spain. You'll have time to visit some places that not every tourist goes. A good guidebook will help you choose places that will be especially appealing to you.

I'll leave Andalucía for others to address since I haven't been there recently. At the time of year you're visiting, I'd want to spend most of my time in the south and would focus on seeing it comprehensively. Then the leftover time would be allocated to Madrid and Barcelona.

Madrid is primarily about its three major art museums and the Palacio Real, though it certainly has other things to see. The time you want to spend there will be pretty heavily affected by your attitude toward art museums. I'd say allow for the time you'd expect to spend at those four sights, then add one or two days extra days for the city of Madrid itself.

Madrid has a number of really magnificent day-trip options, however. Any of the top four would be worth an overnight or two if it fits into your schedule: Toledo (huge historic district and my favorite), Segovia, Cuenca (AVE train toward Valencia gets you there fast; book soonest to try to save a bit on the fare), Salamanca and Avila. With as much time as you have, I honestly would say the first three are almost must-sees, though in the case of dreadful weather not suitable for outdoor wandering, I'd probably abort the trip if I hadn't pre-purchased train tickets. I found Avila only a 2- or 3-hour destination and much less interesting than the others. I have not been to El Escorial. Everything I've mentioned can be done readily by train, but if you wanted to make a multi-day loop to several of those places, a car might save some time.

Barcelona has dozens of modernista sites, quite a number of which you can go inside (payment required). I am irrationally fond of them and therefore spent 10 days in the city, which wasn't enough for me. Only you know how many of those places you'd like to see. Although it doesn't have a Prado, Barcelona's museums are many and varied, and it has historic districts far older than anything you'll find in Madrid (discounting the Egyptian Temple). I think Barcelona needs considerably more time than Madrid, not counting day trips.

Enric has explained to us that there really isn't a slow period for Barcelona. Therefore, I'll issue the same warning we give to folks headed there in mid-summer: Quite a lot of the modernista sites have long lines if you don't show up equipped with a ticket. In my experience they don't sell out weeks early, so you need not worry about buying tickets right now, but these are generally considered places where you should buy tickets before arriving at the site: La Sagrada Familia (separate ticket to climb one of the towers), Parc Guell, Casa Batllo, Casa Mila (aka La Pedrera), and the Picasso Museum. The Tourist Office sells tickets for all except the LSF tower-climb, I think, charging a 2-euro service charge per ticket, or you can buy online.

The T.O. has a handy list of all the local museums and sights that are free one day a week or on the first of the month.

Some of Barcelona's key day trips are Girona (beautiful historic town), Montserrat, and the Dali sites in and near Figueres and Cadaques. Montserrat is at altitude so could be cold in Feb/Mar. All of the listed places are visitable by train/bus, but the Figueres/Cadaques combination would be challenging in a single day. It would be easier, but still not terribly relaxing, if you were based in Girona for a few days (which I recommend) and day-tripped from there.

Edited to add: Somehow I always forget Tarragona, which has important Roman ruins. It's an easy day-trip from Barcelona, too.

It's good that you are planning an extended stay of up 2 months - you will really get to 'experience' the countries (yes, more than one). It make sense to start with the 3 big cities - stay 2 weeks in each.

2 wks Barcelona - perhaps a car for a few days visiting the Costa Brava. Sitges and Tarragona are easy by train.
2 wks Madrid - day trips from here are easy by train to Toledo, Segovia, Avila, El Escorial, Salamanca & Cuenca.
2 wks Seville - day trips from here are easy by train to Cordoba, Jerez, Cadiz, plus Italica & Arcos by bus.

Now a car is best for your last two weeks, sweeping from Seville through Ronda (3N) and the 'pueblos blancos' to Granada (3N), before the coast at Nerja (5N) and finishing in Malaga (3N) to fly out.

Hopefully by late March you will benefit from some warmer days on the coast. You could base yourself for 2 weeks somewhere near Malaga/Nerja, but you will need a car for your days out, and the driving times will be considerable. In this case you might like to plan a couple of overnight forays to Ronda and Granada.

I also don't know what you have in mind when you say "southern coast." While Spain isn't as big as Canada, it is a large country by European standards. As others have said, spending 2-3 weeks each in Madrid and Barcelona is fine, lots to see in each city and lots of day trips. Madrid's sights tend to be fairly concentrated but Barcelona's are spread out, so there's no ideal area - maybe near the train station if you are planning a lot of day trips.

Must-see lists are for short visits. You don't have that constraint. Invest in some good guide books. RS books are a good start, especially if you haven't traveled much in Europe before. I like the DK Eyewitness guides for cities.

I agree with other posters that a good guidebook for Andalucia will be very helpful. I have found the one by Lonely Planet to be excellent. I spent several weeks recently in that area, staying in Cordoba, Sevilla, Cadiz, Jerez, Malaga and Ronda and I found that train connections are generally pretty good. A car really isn't necessary as you could also choose travel by bus. The weather in the area should be about the best in Spain during your late winter, early spring trip. With weather as the primary consideration, I would recommend you begin in Andalucia, then proceed to Barcelona and then Madrid.

The thing with Andalucia is that some of its best sights are not day trips from a single location. Sevilla would be the best choice, but Ronda, Granada and the Med coast are not day trips.