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Let's divide the route into 3.

The first route is from Chennai to Bangalore. The second is from Bangalore to Mysore and the third route is from Mysore to Coorg. All three stretches are quite different from a driving standpoint. For the last 2 stretches (that is Bangalore to Coorg)  see Bangalore to Coorg by Road for more detailed driving directions.

Chennai to Bangalore Route (Distance 328 , Driving time 6hours ) :  Chennai City --> 36km --> Sriperumbudur -- 30km --> Kancheepuram -- 42km --> Ranipet -- 24km --> Vellore -- 118km --> Krishnagiri -- 54km --> Hosur --- 24km --> Bangalore ( NICE Expressway entry (bypass Bangalore city) )

Bangalore to Mysore Route (Distance 147km, Driving time 3 hours):Bangalore ( NICE Expressway entry)-- 25km --> Kengeri ( NICE Expressway exit ) -- 82km ---> Mandya -- 40km --> Mysore city.

Mysore to Coorg (Distance 100km, Driving time 3 hours): Mysore –> Yelwal –> Hunsur –> Kempalapura –> Piriyapatna –> Bylakuppe –> Kushalnagara –> Suntikoppa –> Madikeri

• See Bangalore to Coorg by Road for more details, esp note the two ways to to bypass Mysore city.
• 23 Places to Eat on the way to Coorg! for the restaurents and drive ins between Bangalore and Coorg.