Where else other than Madrid?

You might consider Valladolid, which is about an hour northwest of Madrid by train. I was there some years ago and it’s a lovely city with a lot to see and do. And I would imagine, although I don’t know for sure, that it would be considerably cheaper than Madrid.

Or you might consider Costa de la Luz or possibly Valencia, which are farther south, if you’re looking for warm weather. Both should be cheaper than Madrid. Costa de la Luz is on the coast and has beautiful beaches.

Madrid is my least favorite place in Spain. It looks like Barcelona and Seville are each approximately 2:30 by train from Madrid. I would suggest you take a look at those.

Have you been to Spain before? Madrid? Madrid is a pretty city, but if you aren't interested in the museums, I think other areas of Spain are far more atmospheric and cultural. This time of year, I think I'd go to Andalusia. Sevilla, Cordoba are a quick train ride from Madrid. Barcelona is close by train, too. I really liked Barcelona and the neighboring cities that we visited, but I felt it was more expensive than Madrid.

For pricing, consider looking at places away from the major urban areas that most tourists gravitate to. As mentioned Valladolid is an option as are Logroño, Manzanares, Plasencia, Trujillo, or Zamora. There are others.

I believe Madrid and Barcelona have the most expensive hotels in the country, as a general rule.

From the weather standpoint I'd prefer the south at this time of year. Take a look at lodging costs in Cordoba and Seville. If you want the coast, Malaga can be considered. Seville has the largest number of sights among those cities, I think. I don't know how lodging costs will compare.

Don't forget to check rail fares. They can get rather high for late purchases. Cordoba will be cheapest, then Seville, then Malaga--assuming you take express trains.

I wonder whether lodging costs might be lower in Alcala de Henares than in Madrid. Alcala is virtually a suburb; it's connected to Madrid by cheap, frequent commuter trains. It's an historic university town with an attractive historic center. You'd be close enough to Madrid to commute in for sightseeing.

As others have suggested, once you get away from the capital (and other major tourist cities), it does get cheaper. Although, even then, I suspect you'll find some "sticker shock" compared to Europe a decade ago (or Thailand today).

As well as the places already mentioned, I'd add Burgos, Salamanca and Avila.

However, late November isn't the best of weather in that region. And it certainly isn't ideal for "warm weather people".

You could go South such as to Murcia or Andalucia, but it still won't be "hot" by any means. For that you could fly straight back to and then from the Canary Islands. As well as being an interesting part of Spain, they are better for "winter sun". I haven't checked, but there will be regular flights to/from Madrid airport.

Madrid has the Prado and some historical sites, but nearby Toledo is FANTASTIC. It was Spain's capital until 500 years ago when it was moved to Madrid. Therefore, the city is pretty much preserved its medieval charm. It is my favorite city in Spain. You can do a day trip from Madrid or stay there (recommend two nights).
Also, Segovia and Avila, north and northwest of Madrid can be done in a full day.

The best alternative outside of central Spain is go south to Cordoba and especially Seville. Seville is wonderful..

Consider doing Sevilla-Granada-Barcelona-Madrid (before your flight back home).
Fly/train to Sevilla the same day you land in Madrid leaving all your Madrid days for the end.
Three nights in each will give you a flavor for each city if you don't try to see everything.

I'd seek out recommendations for neighborhoods in Madrid where you might target your search. I am sure other towns would be less expensive, but some Madrid suburbs might be comparable with the rates in some of these attractive cities. And the transport ease you would give up may not be worth it.
I usually target my searches at around 100 euros per night when I am on vacation, so that is a normal rate.
Just based on some of my past trips or tentative trip plans, I'd say try Tarragona.

You would have to add the train/bus cost to go to/from Madrid to Estepona, but it looks like there’s some much less i expensive options there, plus you’re in a warmer area.