The Drive to Chikmagalur is definitely worth it, Chikmagalur is 252 kms from Bangalore and there are two routes available one through Hassan and the other through Arsikere
The best route is through Hassan, you have 4 lanes upto Channarayapattna and from there till Chikmagalur the road is two lanes, the roads are well maintained and you have 4 toll gates in total
The reason Hassan is the best route is because you can visit World Heritage sites like Shravanabelagola, Belur and many more. Also you could visit the highest peak in Karnataka- Mullayanagiri which is about 21 kms from Chikmagalur, you could also visit Kemmannugundi, the drive from Chikmagalur to Kemmannugundi is mind blowing since its takes you through the most remote forest of the Bhadra wildlife sanctuary - a photographers paradise
It all depends on how you would travel, how many days would you travel and so forth.....