Eating Madrid at Ten at Night
The single most common complaint about Madrid is that the food is fine but the atmosphere is missing. It is a scheduling problem.
The timetable is the culture
Lunch is the substantial meal, it starts around two and it takes as long as it takes. The afternoon slows down. Dinner does not begin at seven, it begins somewhere around ten, and the bars fill afterwards rather than before.
A visitor arriving at a restaurant at half past seven is not eating early by local standards, they are eating at a time when the kitchen may not have opened. The room is empty, the service is unhurried in the wrong way, and the conclusion drawn is that the city is overrated.
None of this is difficult to accommodate. It just has to be deliberate, because your body will not do it by itself for the first two days.
How to shift, practically
Eat a real lunch on the first day, as late as you can manage, and then simply do not eat again until nine. You will be uncomfortable once. After that the rhythm holds by itself, because the late lunch is doing the work of keeping you going.
Use the afternoon the way it is intended, which is not for sightseeing at pace. This is when the parks and the quiet neighbourhoods are best, and it is also when almost nothing needs to be booked.
The reward is that at ten in the evening you are hungry, awake, and in a city that is fully occupied rather than half empty. Everything that Madrid is supposed to be is happening at that hour, and it is simply not available at seven.
On the free tapa
In a lot of bars, ordering a drink brings something small alongside it at no extra charge. It varies enormously, from a few olives to something the kitchen is genuinely proud of, and it is the fastest way to assess a place.
Treat it as a sample rather than as dinner. If what arrives is good, stay and order deliberately from the menu. If it is not, finish your drink and move on, because you have just gathered useful information for nothing.
Working a street this way for an hour before committing to a proper meal is, as far as I can tell, roughly how the city itself does it.