i'm a little unsure i can properly take into consideration your preferences and conditions, because they seem pretty violently different than my own. i've moved around frequently on vacations before and enjoyed it, but i much prefer to spend longer in one place. if i had 16 days, i'd say to spend it one city. don't waste your time moving around.
that said, if you are going to move around more i have thoughts on some possible cities within your area.
france.
lyon is really cool.
i was there a long time ago, but i also recommend grenoble. especially if you can get out into the mountains, but also even if you can't. kinda could fit logistically with your time in switzerland.
italy.
rome is unmissable. my wife and i were just back there this spring and although it was pretty changed from how i still remember it from 25 years ago, it's amazing as simultaneously a tremendously provincial city and also the capital of the italy and (still in some ways) the world. i'm an atheist and this last time there, i found the overtly catholic nature of the city pretty moving and the roman era ruins literally everywhere and usually all but ignored as commonplace to be as evocative and charming as ever.
florence isn't overrated.
naples is great.
bologna is fun.
venice is a bit of a disneyland, but it's also unique.
spain.
don't hesitate to hit pretty much any spanish city or town of any size. hard to go wrong. not getting bombed to crap in ww2 is a big advantage.
i could easily spend two weeks in madrid and wish for more time.
barcelona i thought was a bit overrated, but it has a nice vibe.
valencia is less touristy barcelona.
santiago is pretty and also has a nice vibe.
i can't not recommend granada (where i went to school). great town and i can tell you where to eat.
