As far as hotels go, is this the type of place you are looking for - https://www.tripadvisor.com.my/Hotel_Review-g3522354-d655458-Reviews-Malihom_Private_Estate-Balik_Pulau_Penang_Island_Penang.html
Bayan Lepas is the airport and industrial area - it has more concrete than greenery.
You're going to struggle to find everything you want in one place so maybe prioritise and compromise. Off the beaten track doesn't really exist here any more and if you want good restaurants in the evening and sights during the day you really need to be in George Town, but then you won't get jungle!
You could also consider the Bellevue Hotel on the top of Penang Hill for a more jungle stay but then you'd be at the mercy of the funicular train (and crowds of tourists) for your transport up and down unless you use their jeep service down to the Botanical Gardens.
The Equitorial Hotel in Bukit Jumbal might be worth a quick look too as it's set up on a hill overlooking greenery.
And finally the Rasa Sayang in Batu Ferringhi has wonderful old rain trees and nice gardens.