First time to Spain (Madrid & Costa Blanca)

Hi!
A few comments on the Alicante/Elche part.
Alicante is safe, no worries there. There is not a ton to do but it is a good place to relax. The castle at the top of the hill is interesting, so is the Central Marker, there are a few museums but I never visited those. I would visit Elche as a day trip from Alicante, it is very easy by commuter train and there is no need to spend more than half a day there to see the palm grove and Huerto del Cura. Instead of staying there, I would stay in Valencia, and come back to Madrid on the 15th rather than the 14th if your flight is on the 16th. It is a less than 2-hour train ride.

Hello, and welcome to the forum.

There is SO much to do and see in Madrid and just three full days will mean you'll have some major editing to do. Early September will still be quite warm, and for that, you might need to slow the expectations of your pace. I certainly would stay near the airport at the end of the trip—you'd be giving up "out the door" access to the city just to save 15-30 minutes on your departure day.

Accommodation that's near the action but away from "touristy" is a little tricky—it's a compact city center, so you're kind of in it or out of it. Also, note that among all those tourists are also loads of Spaniards and Madrilños living their daily lives in the center. I'd suggest looking to the east/west flanks, near Opera/Palacio, or towards the museums/Atocha. I actually think the Las Letras neighborhood is the best location for visitors to stay: central, fairly local, lively without being rowdy.

I'd skip the Rastro- it's not really a good, vintage flea market—mostly mass-produced tat. The sunset at Dibod is nice, also at the San Francisco Gardens, next to the Royal Basilica of San Fransico.

Madrid is certainly a massive city, but it is quite manageable if you take advantage of the superb Metro. The Metro is fast, clean, cool and unlike other cities is pretty easy to navigate. You’ll see most of the major sites are on the same line. I’d make sure your accommodations are a short walk from a Metro stop. I also found that while wandering around, you’re mostly drawn towards the center of town: Plaza del Sol, Plaza Mayor, to the Royal Palace, along Calle Mayor. That’s a bit more bite sized for exploring. The area around Plaza Santa Anna is terrific for eating, particularly nice in the evening.

Sights are aplenty. You haven’t mentioned the museums. The Prado is one of the world’s great art museums, and imo would be crazy to miss. Seeing Guernica at Reina Sofia is amazing, and if you focus on that it can be a short visit. I enjoyed the Royal Palace as well, it compares favorably with other opulent European residences. For a truly memorable experience, attend a bullfight.

I’d skip Rastro market. You might want to look into getting some suckling pig in Toledo. I’m not familiar with the restaurant you mention, but these “world-famous” restaurants in capital cities can be expensive and underwhelming. A smaller restaurant in a smaller (though still touristy) town might be a better experience.

Getting to Barajas from Madrid can be a bear, but I would not stay at the airport at the cost of an evening in Madrid. At least consider a taxi for a night out, or to the airport if you’re concerned about getting to the airport.

I second what awrzesinski suggested. In April, I stayed at Hotel Europa in Madrid, which is in the RS guidebook. It's clean & furnished nice, has a hotel restaurant, is walking distance to most of the sights (excepting The Prado and Sofia Reina) and next to Plaza del Sol and a Metro stop. For the Temple Debod visit, take a taxi from your hotel or a taxi from the metro stop. It's a long walk and a big park.

In Toledo, take the tourist "train" to get an overview of the town. Be sure to see the Toledo Cathedral, reportedly once the best in Europe. The high altar and choir seating are amazing! The Army museum collection was not fully open because of the recent fire, but the reduced admission price reflected this. Part of the highlights on display were historical battle uniforms, some battle and ceremonial swords. The museum is built over the original town fort walls and castle. Interesting adaptive re-use. You can take the elevator in one of the corner towers for city views. Note that there are many weaponry stores in town, all the more for bargaining. I was told that there is a current use sword foundry near the bus station, but I had no time to get there for a possible tour. I enjoyed my stay in Toledo.

Definitely have suckling pig at Botin in Madrid. It's really worth doing, even if you never do it again. I believe they also have lamb as a specialty. Delicious - both. Can you fit Segovia into your schedule? You'll find plenty of swords/knives stores in Toledo - almost every where you look.

Re safety:
There are two aspects to consider. One is bodily attacks, which I believe are quite rare. The other is petty crime, like purse snatching and pick -pocketing, which are quite common. Somewhere on this site there is advice about avoiding the latter. Read it, and do as it says.