Shivamogga!
Shivamogga is called “Malenaadina Hebbagilu”or “Gateway to Malnad”.
Shivamogga lies on the Banks of Tunga River and is landlocked by beautiful places like Chikkamagalur, Haveri, Udupi, Uttara Kannada and Davangere.
It is approximately 300 KMs from Bengaluru and there's excellent transport facility between the two cities. 3 Intercity trains run between the two cities and KSRTC buses (Suvarna Karnataka, Rajahamsa and Airavatha) are available every half an hour.
Accomodation isn't a problem either. Shivamogga is a well developed city with plethora of 3 Star hotels available at reasonable rates.
Off the top of my head, some of the really famous and beautiful places to visit in and around Shivamogga–
1. Jog Falls - It is the second highest plunge waterfall in India. It is around 100 Kms from Shivamogga. Can be covered in half a day.
2. Gaajnooru Dam - Lies in the outskirts of Shivamogga. Hardly half an hour drive from the city, this dam is built over Tunga River.
3. Aagumbe - It is called the "Cherapunji of South India" and well, the picture speaks for itself!
4. Kodachaadri - A mountain peak covered with dense forests in western ghats. This place will take your breath away. 8)
5. Bhadra River Project Dam - The backwater scenes are prettier than the dam.
6. Taavarekoppa Safari - Tigers and lots of deer!
7. Linganamakki Dam - Another dam built over Sharavati!
8. SakreBailu Elephant Camp - 30 minute drive from the City, lies on the banks of Tunga River on Thirthalli Road
9. ThirthHalli - Of huts and Cows and Rivers and trees and hills and Bridges!
10. Hidlumane Falls (Kodachaadri)- Just look at it! :')
11. Sharavati River
12. Kavaledurga Fort - Ruins and Greens.
13. Koodli - A place where Tunga River and Bhadra River meet.
You can cover 3-4 places in a day since most of them lie very close to each other and share same routes.
Jog Falls, Gajinooru Dam, Sakrebailu and Taavrekappa Safari all lie on the same route.
BRP dam and Koodali Sangama are 30 minutes drive from the city and both can be peacefully visited within 3-4 hours.
Do justice to Aagumbe, Kodachaadri and Kavaledurga by reveling in its beauty for at least a day! :)
I suggest you book a cab/tempo traveler instead of travelling in the local buses. Cabs are pretty inexpensive and will provide flexibility in timings and are any day more comfortable than the rickety buses driven by really rash drivers. Travelling in western ghats is super fun: spectacular greenery, and you'll come across tiny waterfalls alongside roads which will make you want to get down and just be!
Malenaadu is the best refuge if you want to get away from the city frenzy. These magnificent beauties will inspire you, restore your faith in life and provide you with a sense of purpose!
Wishing you a happy journey and a wonderful time with your friends and family! :)
Source - Wikipedia
Image Source - Google