Flying in/out of Madrid, 9 days in July 2017 with teenager, Best day trips, or overnights

Segovia, Toledo, Cuenca, Salamanca

If you want to get out of Madrid for a couple of days, I would suggest taking the train to Seville and spend 2-3 nights. You can see the sights in Seville (Cathedral, Alcazar, tapas crawl, etc.) for roughly 1.5 days and then spend a day exploring Cordoba (Mezquita, etc.) on the way back to Madrid.

I think the previous responses have nailed the top day-trips and probably the top 2-day side trip (some might argue for 2 nights in Toledo). But since you mentioned small (note: the historic district in Cuenca is not small but feels like a small town) or off the beaten path, here are two places I enjoyed in 2015:

• Alcala de Henares, an old university town with a very pretty historic distict. It's a fair-sized place but not large. Accessible by train.

• Chinchon, a quirky sort of place that is reportedly popular with folks from Madrid on weekends. The main square is round and is or was used as a bull ring. There's some sort of food connection (maybe suckling pig). Much smaller than Alcala de Henares. Accessible by bus.

I didn't go to any specific sights in either place; I just wandered around, enjoying being somewhere that provided a major contrast to bustling Madrid. Honestly, I would choose the places already mentioned (among Spain's top destinations) before these.

Re: Cuenca -- it's a relatively quick trip via the AVE that goes on to Valencia. Those tickets are rather pricey if not purchased far in advance. There's a regional train, too, that's not expensive, but it's far too slow for a day-trip. The AVE station is far enough outside Cuenca that it's not walkable. There's a bus but I think it runs less often on Saturdays and possibly not at all on Sundays. So either verify bus availability ahead of time, avoid going to Cuenca on a weekend or holiday, or budget for a taxi. Not too many Americans have discovered Cuenca so far, which I think is fun. It has an interesting cathedral, hanging houses along a ravine and two good modern-art museums.

July is hot! Seville in particular. Check wunderground website for historical temperatures for 'your' week for Seville or wherever you are considering. Cuenca appears to be a hill town, so may be a little cooler than Seville, but you may need to ensure you have AC. If you score lodgings with a pool, you can utilize that for those siesta hours in Seville, buy fans and they seem to utilize shade awnings on the pedestrian streets. Things are open late, so perhaps it won't be too bad if you adopt the Spanish siesta concept. I am sure that is where it all started from anyway....avoiding the hottest part of the day.
Avila is often done as a day trip and there is the Valley of the Fallen - though that might be too sobering. If she has read/seen Don Quixote - find some windmills in La Mancha province.

My understanding is that you have 9 nights on the ground, in and out of Madrid.

Day
1. Arrive Madrid (6 nights)
2. Madrid sights
3. Toledo day trip
4. Segovia day trip
5. El Escorial + Avila day trip
6. Madrid sights
7. Train to Valladolid (1 night)
AVE 4099
Dep 09:30 MADRID-CHAMARTIN (Spain)
Arr 10:33 VALLADOLID (Spain)
8. Train to Salamanca (1 night)
TRN18304
Dep 09:40 VALLADOLID (Spain)
Arr 10:46 SALAMANCA (Spain)
9. Train to Madrid (1 night)
ALV 4958
Dep 15:30 SALAMANCA (Spain)
Arr 17:06 MADRID-CHAMARTIN (Spain)
10. Depart Madrid

From spain.info ...

Valladolid
Standing on the banks of the Pisuerga river, Valladolid will astound you with its cultural legacy reflected in the houses, palaces and churches in the old quarter.
What to see...
One of the city's most famous landmarks is the unfinished cathedral, which also houses the Cathedral Museum. We also recommend visiting other fascinating churches such as the gothic Santiago church or the church of Santa María la Antigua.
In the city centre, you'll find the magnificent Plaza Mayor, and the surrounding area is home to many grand houses and palaces, such as The Palace of Los Pimentel and The Palace of the Marquis of Valverde.
To truly understand the cultural importance of Valladolid, visit its University, the College of Santa Cruz or the former residences of famous historical figures, which remain to this day. These include the birthplace of Spanish poet José Zorrilla, the Museum House of Christopher Columbus and the House of Cervantes, where the author of Don Quijote once lived. It is where the writer made the finishing touches to his great work.

Salamanca
Salamanca is a university city par excellence. Simply by walking through its streets you'll feel the centuries of history, art and knowledge. Known as the 'city of thought and learning', when we speak of culture, we speak of Salamanca.
What to see...
Salamanca is the perfect city for exploring on foot, with a historic centre that has been declared a part of our World Heritage by the UNESCO. In the pedestrian streets of its historic quarter you'll see the Casa de las Conchas house, with its unusual façade adorned with over 300 shells, the Clerecía building, and –of course– its famous university. This was the first university established in Spain, and is one of the oldest in Europe. Don't forget to follow tradition and look for the stone frog hidden on the front –if you find it you'll be rewarded with good luck. On your visit to the cathedral you'll see two buildings joined together: the New and the Old cathedral. Get your camera ready, because the mediaeval towers offer spectacular views over the city.

Air conditioning would be essential in all the places mentioned, including Cuenca. The good news is that it's pretty unusual not to have a/c in hotels in those areas, including 2-star places. Just be very careful to check before you book.

I would not go to Seville in July on such a short trip when there are so many other options. The average high temp for the month is over 100 F.

Really, then only way to be nearly certain that you won't be traipsing through miserble (Madrid and surroundings) or worse (Andalucia) heat every day is to head to or near the northern coast (Basque Country, etc.) That, however, is not what people think of as classic Spain and would be an unusual destination on a first trip. You may get lucky with the weather (though I think it's unlikely).