Munich

Shana although you booked Mike's Bike Tour, I would also consider Rick Steve's free audio guide and a food tour at the Vikutalienmarkt.

I know for many visitors from the US, it's important to visit Dachau. Nevertheless, I would always visit the NS-Documentation Center first before going to Dachau (same day would be possible). In my opinion, it's important to understand how something like this could happen and how each of us could help to ensure that something like this never happens again. https://www.munich.travel/en/pois/arts-culture/ns-dokumentationszentrum.
The NS-Documentation Center is part of the Kunstareal, as is the Alte Pinakothek and many other great museums. My favorite is the Lenbachhaus. https://www.munich.travel/en/pois/arts-culture/kunstareal.

If you are at the Theatinerkirche anyway, you can also take a walk through the Hofgarten and visit the Residenz.

A bit outside the old town is Nymphenburg Palace with its fantastic park. I would recommend either the Residenz or Nymphenburg.

Mike's Bike Tour also cycles through the English Garden, so you'll be sitting in a beer garden at the Chinese Tower anyway. Nevertheless, I would recommend you to visit another beer garden becasue nothing is more Munich than that: https://www.munich.travel/en/topics/eat-drink/overview-beer-garden

It would be good to know what restaurants exactly. I assume you want to try Bavarian food, but it's important to know that this isn't what Munich residents typically eat every day. And we don't even go to the Hofbräuhaus... so very few of us do it regularly. So the question is, do you want it to be a typical tourist experience, or do you really want to immerse yourself in Munich life?
Simply Munich has a few interesting things to say about it: "So you've truly eaten like a Munich local when, at the end of your day, you have enjoyed vegan miso mushroom soup, pinsa and Weisswurst. It may sound like a wild mix, but only until you have tried it yourself." I could recommend a lot of restaurants but please just let me know what you would prefer :-)

What's happening in Munich in May: https://www.munich.travel/en/topics/event-calendar/may-street-festivals-backyards

And perhaps you'd like to leave the old town behind and follow the Art Nouveau trail in Schwabing or you want to visit the French Quarter in Haidhausen.
Or perhaps something more modern, towards the Olympic Park, BMW World and museum, or the Werksviertel (behind the Ostbahnhof). Maybe you are also interested in soccer and the FC Bayern Arena and the museum.
I also have an old boat in mind where you can enjoy something to eat and a drink on a warm evening - perhaps I shouldn't mention that this boat isn't floating in the water, but is standing on a disused railway bridge :-)

Please let me know what interests you, then I can post more links.

Shana
You might like a recent post of mine about things to do and where to eat in Munich. See https://community.ricksteves.com/travel-forum/germany/first-time-visit-to-munich-germany-where-to-stay-near-sights
A couple other suggestions for traditional Bavarian food are Altes Hackerhaus (right in the old town between Marienplatz and Sendlinger Tor) and Hofbräu Keller (not the Hofbräuhaus, but just east of the river on Wienerplatz). Altes Hackerhaus has delicious, crispy-on-the-outside and melt-in-your mouth pork knuckle „Schweinshaxe“) and Hofbräu Keller does a lovely roast duck. And neither place will break the bank.
If you find yourself up by the university near the Schwabing neighborhood, stop in the White Rose (“Weiße Rose”) museum on Geschwister Schollplatz.
Not nearly enough Americans know about the white rose Nazi resistance movement and two of its most well-known victims, brother and sister, Hans and Sophie Scholl. You can visit the museum and their memorial in 30 minutes or less.

Weissewurst before noon; remember that.

I think everyone should see Dachau, it's something that stays with you. And when some ignorant idiot starts comparing someone or something to the Nazi's you can get grasp on just how inane they really are. But if you spend the rest of the day in a beer garden I'll understand.

Munich is not a city you can get a good feel for in a couple weeks, let alone 3-4 days. There's just so much...I really like it. I used to spend a lot of weekends there. I had good friends who lived there. I still go back.

Go up by the University and visit one of the art museums.
Walk the English Gardens.
Visit the Deutsches Museum. It's one the world great museums.
Find a jazz cellar and sit awhile.
See the Residence and Nymphenburg.
Watch the Glockenspiel at 1100.
Catch a concert or play at the State Opera.
Go where most tourist don't and visit Schloss Fürstenried.
Visit the Hunting and Fishing museum (am I the only person who's ever done that?)
Go to the Planetarium.
Go antique hunting north of Oskar von Muller Ring.

Have a good time.

I second the Weisses Rose Museum. My wife and I visited it last fall for about an hour. Kinda like Dachau, we felt like we needed to see it. Especially these days, more people should visit these sites. There is also a Jewish History Museum within walking distance of the Am Markt (good choice for your hotel, by the way). In May, the weather should be nice enough for a visit to the English Garden and a meal at the outside beer garden. You could actually walk to the English Garden from the Weisses Rose. Good wurst haus next to your hotel for a lunch.

and Hofbräu Keller (not the Hofbräuhaus, but just east of the river on Wienerplatz)

Behind the Hofbräukeller, you'll find a fantastic beer garden - my favorite.
Tables with tablecloths are with service, while those without are self-service. Self-service means beverages must be purchased in the beer garden but you can either bring your own food or buy it there.

Visit the Hunting and Fishing museum (am I the only person who's ever done that?

Nope. I did as well :-) I've always enjoyed it, even though I don't fish or hunt. I like the building, and of course, as a child, I loved the wild boar in front ot the museum.

white rose Nazi resistance movement / I second the Weisses Rose Museum

Well, that leaves me speechless in a really positive way. I wasn't sure whether I should suggest it to anyone, or whether it would be of interest to visitors. As a Munich native, this is really close to my heart, and I'm happy for anyone who's interested in it, too. Thank you.

I hiked to the Chinese Tower in the English Garden. The tower is next to some kind of restaurant or beer garden with a lot of outdoor seating. I swiftly hiked away because there was a horrible stench of cigarette smoke in the area.

In the Munch residenz museum, there is one right way to go through the museum. They don't let you go backwards on your tour. If you skip ahead to use the bathroom, they don't let you go back to continue your tour from where you left off. If you go back to the entrance after skipping ahead, they don't let you re-enter on the same day.

I did not eat restaurant food even once in my 15 night trip. I spent 5 night in in Munich and then moved on to other towns. The money I might have saved is just a coincidence. The vast majority of restaurant food is made with salt, oil or added fat, and/or sugar or less commonly other sweeteners. I didn't have to go far out of the way to find grocery stores that had an adequate selection. Three 3 of the 5 places I stayed at were apartments that had a stove and a little but well-equipped kitchen.

I went to Dachau concentration camp. Victims were supposed to suffer and die at the camp but it wasn't one of the 6 nazi gassing centers, but be sure to walk far enough to see the bath house that the nazis renovated into a gassing facility near the end, intending to gas the remaining prisoners, but the camp was liberated just in time so there weren't gassings.

The Egypt museum occupied me for almost 3 hours.

I didn't end up fitting in the Nazi documation center but I had done some background reading.

I adequately toured the Nymphenberg palace and property even though I doubted I would make time for it.

In the Munch residenz museum, there is one right way to go through the museum. They don't let you go backwards on your tour. If you skip ahead to use the bathroom, they don't let you go back to continue your tour from where you left off. If you go back to the entrance after skipping ahead, they don't let you re-enter on the same day.

After reading this the first time, I tested it out. It wasn't a problem that they let me use a restroom during the tour - I was going back. Perhaps it was a communication issue.
The current problem is that there are renovations going on, and barrier-free restrooms are difficult to access during the tour. You have to ask the staff - this is what the Residenz museum is mentioning on their website.