Is there any way you can trade some or all of your days in Geneva for more time in Rome?

Or, if you're going to be in Geneva for "a few days," can you be in the Alps somewhere between a couple of hours and half a day's drive from Geneva instead? Or at least make day trips from Geneva?

I often tell people Geneva's the opposite of NYC -- it's the place you'd love to live there but hate to visit (N.B.: I know NYC is not necessarily a bad place to live). I don't think there's a single can't-miss tourist attraction in Geneva.

On the other hand, Rome has enough of the "obvious" places you mention to keep you occupied for your entire stay. Although there are a few less-obvious gems as well.