What period of the year will you be visiting? I ask because both areas are well-explored but definitely visiting in the off season can make even some of the same places feel like hidden gems considering the reduced number of visitors.
If you already have a place in Chianti booked for your week, I would suggest starting from there - exploring the roads around that villa you will be able to discover the small wine producers and olive oil makers in the area that cannot be found elsewhere. You will be excited to discover many of them only sell locally and are true hidden gems from the masses, and international markets.
If you ask the place where you're staying at for recommendations of places to ear nearby, you will also discover that there are many restaurants along the roads that offer good country home dishes that are delicious and hidden gems. Many of these places do not ever publicize themselves but are well known to locals - and they are jealous of telling too many people about them, even if they will be proud to share by word of mouth.
As far as scenic roads - my, that's hard because the majority of them are!
If you take a look at a map and roads in the area, take the lesser roads across the area and you will have scenic views for most of the time. There are lots of woods in Chianti mixed in the vineyards, and lots of hills.... so you will be exploring areas that one moment seem to be hiding everything and the next moment after a turn or bend discover a breathtaking view.
This is a hard question because the only way to share is to just tell you to drive - and you will find them on your own!
I could send you to specific spots - but those are definitely ones that are not "hidden" and are easy to find.
Enjoy the drives across the area!