16 Days - Best of Switzerland/Austria/Germany?

You can really cover some territory in 16 days. If you're looking for the Bohemian lifestyle, Munich should be the center of your trip. I often will avoid Switzerland due to it being a little out of the way--and very expensive to travel in. The Austrian Alps are 90 minutes south of Munich and they're just as scenic.
There's enough to see in Munich for 4 days minimum, with great beer halls and palaces to visit. We also have gone to Dachau a couple of times over the years.
Southwest of Munich about 45 miles is the incredible Andechs Brewery--an authentic beerhall run by The Brothers. We also love traveling south of Garmisch around Innsbruck.
The incredible Grossglockner High Alpine Highway should be open about the time you get there--south of Zell-am-See, and it's the second highest point in Europe. The southside of the mountain is the most beautiful place I've ever been.
With the time you have, you could also swing up to Salzburg where the Augustiner beer hall is.
The mountains are best visited by rental car.
We went to Prague/Vienna/Budapest 2 years ago, and all of those are incredible cities for what you're looking for. Train service is also good. The grunge bars of Budapest are frankly hard to beat.

No Swiss huh? I had included it because Rick's shows make it look pretty awesome. I can definitely skip it if you can see/eat/drink the same kind of things in Germany/Austria.

I think it might be more useful to keep your original post going, just adding to it as your plan takes shape. That way everyone sees what stage you are at and how things have evolved.

"I'm mostly interested in food/beer/wine/mountains/countryside..."

The first 3 are available everywhere. But if you're into breweries and wineries where the stuff is created, you should check out the wine regions just west of Frankfurt since you'll be using FRA, and you should check out the breweries in Franconia (northern Bavaria, not so far from Frankfurt either.)

Scroll through the videos on this page that describe the Moselle, Rhine, Nahe, and Rheinhessen wine regions:
http://flyhahn.com/regions/holiday-regions-germany-frankfurt-hahn.htm

The Rhine is an excellent place for hiking/walking in attractive countryside:
Rhine Castle Trail (Rheinburgenweg)
Rheinsteig Trail

Nuremberg's Franconian Bierfest:
https://tourismus.nuernberg.de/en/erleben-geniessen/events/feste-maerkte/d/fraenkisches-bierfest.html

Nuremberg pubs:
http://www.europeanbeerguide.net/nurnpubs.htm

Bamberg (near Nuremberg) pubs:
http://www.europeanbeerguide.net/bambpubs.htm

Bamberg Brewery-inns:
http://en.bamberg.info/brauereigaststaetten/

Hiking in the Bamberg countryside:
http://en.bamberg.info/wandern/

Forchheim, May 21, starting 13:00:
Tag der offenen Brauereien - Open Brewery Day - 3 small breweries offer tasting all afternoon, free shuttle starting at the Rathausplatz (Town Hall Square) in Forchheim:
http://www.forchheim-erleben.de/upload/downloads/pdfs/shop/Flyer_Tag_der_offenen_Brauereien.pdf

In May the Alps are sometimes OK, sometimes too damp.

Any advice on the best city to start or base out of? I'll be flying out of Bologna. And anyone know about reciprocal car rental drop off in those 3 countries, i.e. rent a car in Switzerland or Austria and drop off in Frankfurt?

Cars rented in one country and returned in another country will have a surcharge. On this Forum, I've seen quotes from €50 to €600 (not a typo - six hundred euros!). Cars rented and returned in the same country (even in different cities) usually have no surcharge.

So, you can plan a circle trip, you can plan on renting separate cars for each place (connecting countries with trains) or you can use one rental car for the trip and just pay the extra fee. Once you know your exact itinerary, others can suggest which would work best.