Looking for a beautiful drive along the way

You don't say how long you have to make this trip. At its fastest it's going to take at least 6.5+ hours by the most direct route (and probably more). Frankly, doing the journey in one day ....or even two....won't give you time to see anywhere in a 'leisurely' manner. You could easily spend 6.5 days travelling between the two cities and still not have anywhere near enough time to see all the places worth stopping at on the way.
Also, you simply can't drive through the historical centres of any Italian city nor the vast majority of Italian towns or even quite a lot of villages The majority of Italian settlements have restricted traffic zones...ZTLs...in their centres with, in most cases, CCTV cameras and automatic fines.
Driving down to the coast really is a long way out of your way. Unless you are desperate to do that...and assuming you are taking more than one day... I suggest you try:
Geneva through the mountains via Chamonix-Mont-Blancand Aosta to Turin (which has a fascinating historical centre). 
and/or Milan or, much better imo, less-visited Pavia a hugely atmospheric town full of wonderful architecture and history.
From there you could either:
a) Go north via wonderful Bergamo, with its really ancient walled upper town and its slightly-less-ancient lower town, wonderful food and two funiculars
or 
b) Go south via Piacenza, Cremona (both of which are historically fascinating) and/or Parma.
Whether you go north or south aim to end up in Brescia, which has much lovely architecture, many historical sites & sights and a really excellent museum (Museo di Santa Giulia) which has a vast Roman and Medieval collection and also includes the excavated remains of two Roman villas.
From Brescia you can travel to Verona, Vicenza and especially wonderful Padova (Padua). All three are historically and architecturally fascinating, though I personally much prefer less-visited Padova to the much-more-popular Verona.
And then you can drive across the causeway to Venice, leave the car in one of the parking garages and rely on your feet to get you around! :-)
Whichever route you take you'll be spoilt for choice. But I'd note that if I hadn't already visited any or most of the places I've mentioned above, I'm afraid Genoa would certainly not be on my list. It's historically interesting in its own way but not a patch on the Italian places above.