Hi,
For super family friendly, I would look at those that have an outdoor terrace (if your upcoming trip is in spring, summer or fall). And it depends on the age of the children, of course. And Sunday evenings are tough for family-friendly restaurants, many of which are closed.
So if there are small children in tow, you might want to go to La Florida in beautiful Retiro Park, that has multiple dining venues, the most family friendly being La Galerìa, where kids have plenty of room to wander and to enjoy the many attractions of Madrid’s most beautiful green space…
or to Café del Río on the banks of the Manzanares River with views of the Royal Palace. The bonus of these two is that there is plenty of room for the kids to roam and where families do congregate on weekends.
And consider the Galería Food Hall inside the Canalejas building attached to the Four Seasons, in the center of the city, as downstairs it has multiple venues for those diners of all budgets, from paella at St James to Galician food at Taberna Garelos to other even more informal spots. The best part—it’s open daily with long hours.
If you have teenagers with you who love pizza, the Grosso Napoletano mini chain with 8 Madrid restaurants would fit the bill. The Hermosilla branch, in the elegant Salamanca district would be central.
Or in the Latina district of Old Madrid, the Bacaro de Fabio Gasparini on the pretty Plaza de la Paja is family friendly.
https://elbacarodefabio.es/latina/
If there are teenagers in tow, they would love the look, the buzz and the ambience of the Italian Bel Mondo on the very upscale street of Veláquez, number 39, in the Salamanca district. It’s very, very popular and with an over-the-top decor and a cool outdoor terrace.
As to one dining experience w/o family, it really depends on your dining budget. There are several fine Michelin stars, many more restaurants with 1 Repsol sun, too many to mention here actually, but the restaurant that I choose for more affordable than Michelin star prices and fine consistency is LAKASA, which never fails me. It’s just a fine modern bistrot.
A step above in price would be LA BIEN APARECIDA on tony Jorge Juan, Salamanca district’s most elegant “restaurant row”. I usually recommend it because it’s open on Sunday evenings and has a lovely outdoor terrace. It sports 1 Repsol sun and comes Michelin recommended (but no star).