2 Week Trip - tips? Must sees? General Help?

The only must sees are the places you want to visit. Don’t visit a place just because somebody said you should. To get more ideas look under “Things to see” for each city on TripAdvisor. Maybe something will peak your interest.

In all the main tourist areas you’ll be perfectly safe, even in the evening when the entire town is out walking. There are areas you should avoid by yourself, but if you stay to where the crowds are, you’ll be fine. If you spend 45€ on a meal you’re in a decent restaurant. You’ll have no problem finding restaurants in your price range.

Pickpockets are everywhere so you just need to be aware, especially any time you’re in a crowd. In mid-April you probably don’t need to buy everything beforehand. Most tickets are non-refundable and it would be a shame to lose money if part of the plan changes. In April, there are very few sites e.g., the Alhambra, where tickets need to be pre purchased.

I can't address everything in your query, but as to a couple of points:

First, I've visited many great places in Spain where you will find "old architecture, amazing churches, and culture rich areas to people watch," and where the people you will watch will be the local residents, not what the tour buses disgorge; but while historic and aesthetic enough, they were not the conventional "must-see" towns with the grand "must-see" visual spectacles. (Examples would include Caceres and Zafra in Extremadura, and Teruel in Aragon.)
Second, though I can't give the perspective of a female traveller, I've made several solo trips to Spain and never felt unsafe. In many Spanish cities and towns, everyone goes out among the tapas bars late into the night, and if you go where they go, you'll probably be all right. But do be wary of pick-pockets.

Though you will be a "real tourist" if you stick to the "must-see" destinations, a few tips (even if they are not original) on not being a "horrible" one:

[1] Don't demand that everyone to speak English with you, or insist that they ought to. You're in Spain, and Spanish is the language there. (Along with some Catalan, Galician, and Basque.) If you don't already know Spanish, at least learn some basic words and phrases that you can use to begin an interaction in Spanish. [2] Don't get uptight about minor problems. I don't know whether you're American, but if you are, don't make a big angry deal about "getting what I'm paying for" if some little thing is wrong in your hotel room. (Though there's nothing wrong with courteously calling it to the staff's attention, then ceasing to worry about it.) [3] Along similar lines: if you do stick to "must-see" destinations, you will probably be one of many tourists that hotel and restaurant staff deal with, and while my experience is that they generally deal quite well with it in Spain, being a decent tourist means allowing the occasional waiter or hotel person to have an off-day without making a fuss over it.

(As for other "must-see" sites in Madrid, I'll leave them to the respondents that are sure to follow presently; but I'll check in later, and if no one else cites them, I will.)

You need an extra night in Seville.
Be smart with your train timings to and from a single night in Cordoba.

fly in to Barcelona for 4 nights,
fly to Granada for 2 nights,
train to Seville for 3 nights,
EARLY AM train to Cordoba for 1 night,
LATE PM train to Madrid for 3 nights,
fly out of Madrid.

I agree with David. You're way, way short on time in Seville. I consider it a 4-night-minimum city, but I don't know where you're.going to get the fourth night unless the Prado is the only art museum you want to see in Madrid.

I think you're close to over-committed in Barcelona, given that you may well be sleep-deprived and jetlagged that first day.

Thirteen nights is really tight for five destinations.

One specific question I have wondered about is the train. I know in Italy I had to validate the train ticket before getting on the train or I could face a fine. Is that something I need to worry about in Spain? Is the system similar?

You are best to pre purchase your ticket 60 days in advance directly from the renfe site.
No you don’t need to validate your ticket at the platform before boarding the train. You will have an allocated seat in a numbered car, very easy to locate.
The route …. Sevilla >>> Cordoba >>> Madrid …. is well served with frequent high speed AVE trains
Granada >>> Sevilla offers less frequency and will travel via Cordoba.

Have you checked the train schedules? Looking at September 27 (random date), the last morning train to Sevilla leaves at 7.15 am. There is a train at 8.15 to Cordoba, then either a 9 minute transfer to a train to Sevilla or wait for another half hour for the next train. Presumably you'd have to buy separate tickets which may cost more. The question really is if you've worked out when you have to leave each place and when you arrive at the next city, taking into account the time hotel-to-hotel?

I ask because it feels like you are changing hotels too often. Much as I love Cordoba, you should consider staying longer in Sevilla and possibly one other city (Barcelona) and seeing Cordoba on the way from Sevilla to Madrid (you can store luggage across the street from the train at the bus station.

Visit Barcelona sights geographically. Visit Montjuic, then down to Miro, then take the pleasant walk down to MNAC. Allow at least 3 hours for MNAC. There is a nice cafeteria inside that is reasonably priced. Picasso is near the Cathedral, the Palace of Catalan Music is not far from there.

I was unimpressed by the Cordoba Alcazar. After you've been to the Sevilla Alcazar and the Alhambra, you may have a similar feeling. I believe the gardens are nice, but I was there in winter when everything was pruned back. The Cordoba Synagogue takes about 15 minutes (if it's open). Well worth an hour is La Casa de Sefarad across the way.

If you like more modern painting, add the Thyssen Museum in Madrid. They have some Old Masters and a good collection of 19th and early 20th century works, especially impressionists.

I think I will add a night in Seville and cut a night in Cordoba. Maybe add two and cut a night in Madrid as well.

I like to get suggestions on sights, as some are not really mentioned that much and they end up being really spectacular.

I plan on getting train tickets in advance, it's just too early right now.

I had researched random times for trains and from Granada, I was finding more going to Seville instead of Cordoba, so I will check it again.

This is why I asked what I asked so I can have some different perspective on things. Thanks!

Faedus -
No worries about me acting like an angry American or a bad tourist. I am really pretty easy going and respectful of other cultures. Like I said, I have traveled multiple times to Europe, I just haven't been to Spain. I plan on extending my travel attitude to that as well. I get times are not always exact and things come up, I always try to use phrases in the country's language and am a pretty thankful person when helped out. I can't stand seeing people act out over things that are out of one's control.

I would also do 3 nights in Seville and 1 in Cordoba. I loved the cathedral in Seville (make sure to climb the bell tower) and the Alcazar. I would prefer 3 nights in Madrid too. I enjoyed the Rick Steve’s walking tour there, the Royal Palace is amazing. You can stop for lunch at the San Miguel market. Lots of choices there, I had very yummy empanadas (I also don’t care for seafood). It’s crowded but I had no trouble finding a place to sit for one. And later stop at Chocolateria San Gines for churros (both are on the route). A walk in El Retiro park is very nice too. If you want to see Picasso’s Guernica you will also have to visit the Reina Sofia museum. With 3 nights in Madrid you could also consider a day trip to Toledo.