I just did this 3 weeks ago.
I would suggest - Bangalore -> Attebelle - > Denkanikottai -> Anchetty -> Hogenakkal.
This route is scenic and and goes through a forest, and a ghat section. There is a stretch of bad road for around 3 to 4 kms. Otherwise the road is great to drive.
You can check out the route here
This route also takes you alongside the cauvery river, where you can stop and take a dip if you wish.