Need advice for itinerary in Europe

Prague, Vienna and Munich are all great, large European cities, and they're worthy of a minimum 4 days each. Most would also go to Salzburg for a 2 day minimum. Sorry, but you don't have time to take in Switzerland or Lake Como with the time allotted.
We have been to Switzerland a couple of times, but we find travel through the Austrian Alps to be so much easier to navigate and so much less expensive. And the Tirol of Austria is absolutely breathtaking scenery.
You could easily visit the large cities by train. We find renting a car allows us to see much more great scenery in mountain areas.

Thanks for the information. We had not thought of substituting the Austrian Alps for Switzerland. That sounds like a good possibility - and maybe you've even convinced us to drive - but I'm going to have a tough time eliminating Lake Como from the list. I've heard such great things about it.

Your itinerary would be doable but I would rather concentrate on fewer destinations. Also look at the map. Switzerland and Lake Como are somewhat apart from Prague and Vienna. I see your towns like Munich OK, Vienna great, Prague star. If it was me I would replace Munich with Budapest - another star, that way I would have 5 days for each city including day trips and visiting some smaller towns in between and some hiking and relaxing in beautiful scenery. Austrian Alps are certainly beautiful but it is not Swiss Alps which are quite more magnificent. So I would do either Switzerland, maybe Munich and Lake Como or Prague, Vienna, Budapest. I know you did not mention Budapest but it fits to be done together with Prague and Vienna logistically and historically.

but I'm going to have a tough time eliminating Lake Como from the
list. I've heard such great things about it.

Lake Como is beautiful... just like all the other Upper Italian lakes. But they make your trip more complicated, and you can easily find beautiful spots closer to Munich, Prague and Vienna. For example:
Wachau valley (2)
Hallstadt Lake (2)
Wolfgangsee
Königsee
Dachstein (2)

Since most of these places are between Munich and Vienna I would probably skip Prague, rent a car, and spend a few days between the two cities to see some of them.

Prague, Vienna and Munich would leave you with not much time for another place. I assume that from Munich you would want to visit Berchtesgaden (Salzburg) and Fussen/Garmisch. Three days is good for Vienna and perhaps for Prague, but for Munich (with day trips, you need a bit more). Also, I recommend doing the Romantic Road from Wurzburg to Garmisch. It is loaded with wonderful small towns, walled cities like Rothenburg and Dinkelsbuhl.

If you insist on one more place, I love Interlakken, Switzerland.

Thanks so much for the suggestions. We will definitely think of adding Budapest and scratching Switzerland and Lake Como. We had thought we could do it all by only staying 3 days in each place. We stayed in London, Paris, Rome, and Cinque Terre for 3 nights each and 2 nights in Venice and felt like we had enough time, but we didn't take any day trips to neighboring towns. I hadn't thought about making those cities a home base to take day trips to smaller towns and like that idea.

Please keep the suggestions coming. I really appreciate them!