If you like to go on long drives thru' unspoilt nature circuits, why don't you try the Chikmagalur(Baba Budhan Giri, Kemmangundi) -> Kadur -> Bhadravati -> Sagar -> Talaguppa -> Gerusoppa(Jog Falls) -> Manki -> (pristine beaches all the way to) Mangalore -> Sakleshpur -> Hassan -> Mysore route? That would be a 3-5 days trip. You could stay at Chikmagalur, Gerusoppa(the PWD guest house at the Jog Falls), Mangalore, Hassan. You might want to skip Sakleshpur and Hassan and instead return via Mercera(you need to take a detour at a place called Mani towards Puttur.
Alternately, you could go thru' Nagarahole(stay there for a night) and hit the coast somewhere near Thalassery(you could visit Mahe from there). From Thalassery, you could go north towards Mangalore with beautiful beaches and backwaters on the way. There is a old fort at Bekal that is well maintained. From Mangalore you could choose one of the two ways I mentioned below.
There are a lot of beautiful nature spots along the Cauvery River and its tributaries starting with Talakkad, Shivanasamudram, Galibore, Muthatti, Mekedatu and a few more. Check the Jungle Lodges and Resorts web page for the others.
Have you been to any of the Kabini Resorts. I believe its just 3.5 hour drive from Mysore and one of the best locales for a wildlife adventure. I am in this niche of helping people plan "Boutique travel" and want them to stay in unique, heritage-style boutique resorts.
For kabini, here are my recommendations in the same order:
Orange County, Kabini Water Woods, Kabini Kabini River Lodge