Okay, after the off-the-cuff tipps, now for the second part.
Besides the Hofbräuhaus and Schuhbeck at the Platzl, there’s also the Weisses Bräurössl in the Tal (valley) the road that connects the Marienplatz (main square) with the Isartor (city gate). It’s geared towards masses of tourists but serves traditional food.
In order to help you understand the menu, and what I find interesting besides the boring standard fare of pig, Knödel and Sauerkraut, some lesser-known specialities:
Saures Lüngerl is lung from a calf made in an acid way (with vinegar).
Semmelknödelare a speciality of Bavaria (while Knödel generally are a German traditonal dish) are made from left-over rolls (Semmeln) with spices, boiled in water. They can be eaten not only as side dish, but also as Gebratene Semmelknödeln. for this, they are sliced and browned in a pan, together with scrambled eggs, or mushroom sauce (Champingnon).
Käsespatzn(Spatzen with cheese) are a swabian dish: wet noodle dough is cut into the boiling water to form the spätzle, then overbaked with cheese. In traditional Gaststätten, they often serve this in a small iron pan on a wooden board, and with roasted onions on top. It’s very filling!
A Brotzeitor Jause (snack) in a good Gaststätte is served on a wooden plate/board: peasant bread with several kinds of ham and sausage (cold), sometimes gherkins.
Ah, Obazda(smashed), another speciality for the Beergarden! Despite its appearance, it hasn’t been eaten before 
it’s camembert or similar soft cheese smashed with red pepper (hence the colour) and spices. Tastes good.
While we are at it - tatar(raw meat) takes a lot of trust (because it must fresh otherwise you risk spoiled meat) and maybe courage, but it tastes good. Ideally, a butcher you trust grates the meat in front of your eyes, you take it home, mix it and serve immediatly. You can also try at a Restaurant, if you dare.
Another beer garden food: Radi(raphanus - what a weird name). It’s washed, peeled and cut into thin slices, or rather, an uneding spiral, which is a highly valued art if done right. Every couple of slices, you salt it, and then you eat the whole thing.
The foods I mentioned yesterday: Auszogene
Schupfnudeln
Steckerlfisch
Reiberdatschi
Knödel(Dumplings) in general
The Hofpfistereibakery - with an overview of their breadvariants.
Here’s a list of all Beergardens.
A special thing about Munich Beergardens: because of a law to stop competition against established restaurants, real Beergardens don’t serve hot food, they only sell beer. This is a good idea because it means families and people with low income can make their own picnic at home and go to the beergarden buying only the drinks. For those who didn’t make their own picnic, you can buy some foods, like Obatzer, Radi, Auszogene, Brezn, potatoe salad and a few warm dishes like Steckerlfish, Grillhendl(roasted chicken) and some roasted pig stuff. But it’s not a real menu from a restaurant.
However, some beergardens have a different section (with tablecloths on the table and waitresses*) where they joined with real restaurants, and serve real menus there. For example Grosshesseloheis one. You get there by S-Bahn, and sit on the embankment above the Isar in the middle of a forest. Very nice. Afterwards or before, you can walk back along the Isar river - the right side leads to the streetcar, the left side to the S-Bahn. Or ride a bike.
*Strainger already mentioned not being shown a seat - but that’s not only for beergardens, it’s not done in almost all restaurants in Germany. You go inside and sit down yourself at an empty table, unless there’s a sign “Reserviert” (reserved) on it.
But in most beergardens, there’s self-service - you go to the big counters and get beer and food yourself.
A beer hall inside will usually have waiters, but might also have a self-service section. Look either in the menu or at signs on the walls/on posts. Mit Bedienung/ hier/es wird bedient = with service; Selbstbedienung = self service
Also nice to see if the weather is warm: the zoo Tierpark Hellabrunn. It follows a modern principle of showing the animals in natural habitats, with as little fences as possible.
The Westpark (take the U6 subway to station Westpark) is left over from the IGA (International garden exhibition) in the mid-80s. The built a typical alpine hut, a japanese garden (Munich is partnered with Sapporo, among other cities), a Thai temple and many other things.
Left over from the last BUGA (federal garden exhibition) is the park at Riem (take the subway to Messestadt Riem, I think West).
The current BUGA just started in Schwerin, but that’s East Germany.
There’s also the NymphenburgerSchloss (castle) in the north (take a streetcar from Sendlinger Tor). It has not only wonderfully decorated rooms inside (in case it rains), but also interesting gardens outside: the front is top french-style garden, the back is top-style English park (in the evening you can see deer - the Bambi-animals eating grass.)
There’s a museum for Nature and Man (aimed mostly but not only at children) in one wing, a botanic garden to look at flowers and the Porzellanmanufaktur(porcelain production) there. (If you want “White gold” Souvenirs.)
If you do go into the Englischer Garten, but don’t want to see naked people, stay north of the very tip at the Haus der Kunst. Most people (naked and clothed) are between Haus der Kunst and Chinesischer Turm/Hirschau, in the south part. The north part, the Hirschau, is more quieter and thus better if you want to stay alone.
Though the South part has more interesting sights, with the japanese tea house, the Monopteros and the beergarden at the Chinesischer Turm (chinese tower). There are also horse-drawn buggies at the Turm to take rides.
If you want to see real mountains (excepting the Rockies), the closest and easiest from Munich is to take the BOB (Bayerische Oberlandbahn, upper bavarian train) hourly from the main station (Hauptbahnhof) to Lenggries, take a short walk to the Brauneckbahnand ride the cable car to the top of the Brauneck mountain. Dress warm, it’s 1 600 meters high. Also, the cable car is being serviced till 8th of May, though they open it for the May 1st weekend. (The revision is always done between winter and summer season).
Generally, though, May is not yet the time for mountaineering - there’s still too much snow lying around (Brauneck still had skiing on Easter, and the ski tours off the piste is done by alpinists until pentecoast). June, July, August and maybe September are the mountaineering months. You can walk in the flats no problem though.
And whenever you go in the Alps, even with cable car, please obey the safety rules! = sturdy real shoes, warm clothes including anorack, map, knowledge. The Bergwacht (Mountain rescue) has to rescue enough idiots with high-heeled shoes, sandals or t-shirts already.
If you want higher, you go to Garmisch-Partenkirchen to go to the Zugspitze, the highest German mountain, just shy of 3 000 meters. Below zero, so dress very warm. It has a weather observatory with lots of ugly concrete.
Trivia: on most Alp mountain tops, you will find a Gipfelkreuz(cross), often with a metal box that contains the Gipfelbuch (summit book). Real alpinists who hiked up there instead of taking the cable car then write their names, the date and maybe a few words in there.
