Do not worry about research. You cannot do it all for a city like Madrid that has plenty to offer, you will be unprepared will all the research.
For Daytrips I think Segovia is a must, but since you have not said how long you are visited Madrid there are others but for me Segovia is the daytrip I will do again when visiting Spain.
For tapas tour I can recommend
Walks in Spain Tapas Tour which I done on my third visit to Madrid.
I thought was great tour for myself and enjoy myself the night of the tour. I did it because I could not recommend any tapas tours for Madrid as I already had some places I go to for tapas when I in Madrid.
Andres’s tour took us to various local bars, where we were the only tourists to be seen. During the tour we tasted different wines, sherries, meats, fish and cheeses. I even got a small history lesson on Madrid too and found out that I enjoyed sherry which I have not try in Madrid. Probably because I was ordering Rioja and Vermouth. But sherry? I never would have thought of ordering sherry until the tour.
I think a first time visitor to Madrid, Andres tour is a must as it a first time visitor an intro of the tapas scene in Madrid. From talking to the others on the tour, there was like 12 other people, mostly from the U.S., I knew most would not have try the food/drink we had on the tour on their own.
For me those are the best tours to open you mind or taste buds like this tapas tour, to try new things and learn things about yourself too.
Since you are foodies, visit the market in Spain on an empty stomach, El Mercado de San Miguel. It is close by Plaza Mayor. Here you can try different wines and foods and it was the wow factor. As soon as you walk in the first time you say “Wow!” and “Where do we start?”