Here is (I hope) a link to my post about our most recent trip (our third) to Munich last summer. Its a great town,with much to enjoy, with its large parks and the river for recreation and the relaxed feel of the people who seem to be able to balance work and play. I will add some comments down below relating to prior visits etc.
Spatenhaus is close to where you are staying as is Brenners (we have not been) an Italian that I believe VikingKaj used to recommend here and on CH. Since you are coming from Sicily probably Italian food would be a whole different thing. At Spatenhaus, a few years back we dropped in there for late morning brunch on the plaza. I ordered Kaiserschmarrm and it was superb, the whole experience with the great Dallmeyer coffee they serve and the prosperous relaxed customers was very enjoyable. My husband order the leberkase (a very airy light but solid pork thing which I dont care for much but theirs was a good version - I recommend this brunch experience if you can fit it in. Maybe to revive after a visit to the Residenz or the English Garden.
At the Spatenhaus an der Oper resto proper we have eaten inside there 3 times in the downstairs area which is very nice. We have had all kinds of good things there, very good cooking of traditional dishes. Doubt you could do much better anywhere else for pork, potato dumplings, red cabbage, etc etc. Good beef and fish also. I would particularly like to recommend their house potato and cucumber salad, which I have been meaning to try to recreate from recipes online. It is delicious. They also have a resto upstairs that is more formal and I think with a slightly diferent menu - worth looking into.
Re beer, I am also not a beer drinker - except for Radlers which I learned to drink in Munich. I am married to a beer drinker and there is nothing nicer than drinking the very clean Munich beers (not like the nasty american brews) under the trees in a beer garden to cool off on a hot summer day. They make the radlers with the Helles beer and in Munich the also may offer a drink called a “Russ’n” which is made like a radler but with the weissbeer (wheat beer) which is also relatively light. Both are excellent.
I think someone else has mentioned Der Pshorr which is a big beer hall near the Victuelmarkt- serves a menu slightly downmarket from Spatenhaus, we have always had good experiences there. It tend to be more peaceful indoors than on the tables outside which are usually mobbed.
I am sure there are other excellent meals to be had in the quadrant you are staying in - but they havent been discussed here or on CH in my memory. I have been trying to get to a place called Halali, a little farther away, for 3 visits now but we never have any appetite at dinner time I hope you do better.
