What an adventure.
I urge you all to go driving around the Alps for a few days though if you haven't experienced it. It's a grueling day of driving 1,000+ miles driving from the UK if you want to get to anywhere tasty, or the alternative and more civilised way is to fly to Milan Malpensa (£40-£45 return from London most of the time) and hire a car from the airport for the occasion. Can do the same from Geneva if you wish. If you just want to chuck around a fun little hire car and admire the views, then you can hire something like a Fiat Panda / 500 or, Smart ForTwo, Citroen C1 or similar from Milan usually for the grand sum of €10 per day. I'm a fan of the Panda so that is my personal recommendation, although at one point you could hire an Alfa 4C for 4 days for €400!
From Milan it's just a short drive north to Lake Como (Como town itself or Menaggio are nice places to stop at for a coffee) and Lake Maggiore - take your pick or do both. They are beautiful. From there, you've got an almost infinite number of stereotypical Swiss mountain passes to aim for whether you go west (Val d'Isere via Turin?) or north/east to Lake Obersee via Davos. Val d'Isere is a ghost town out of season but if you do visit or go through Val d'Isere then leave to the east and go up through the mountains - the road is absolutely stunning and you'll thank me later. Lake Interlaken is nice to drive around but sadly Interlaken is become more and more commercial every year.
It takes a bit of planning to see them all in the most efficient order so as not to be driving back on yourself but you want to be taking in as many of the mountain passes as you can - Susten, Grimsel, Great & Little St Bernard, Furka, Splugen... just Google 'Swiss mountain passes' and go from there. I've done the routes on a few banger rallies in £500 cars and an old Jag XJR which was quite perilous on some of the tight switchbacks at the top of a mountain. I'm not keen to do it in a coach any time soon
Four days is a good time to aim for I think, allowing for 5-6 hours of driving each day and a few stops in nice places, then look around on Booking.com or similar for a hotel in a place each night, returning the car to the airport at the end of the final day and fly back.