We travelled by road from Bangalore to Mysore took approx 3-3.5 hours. Mysore is cleanest city in Karnataka and you will enjoy beautiful green/blossom flowers and coconut plants all around which is pleasure.
Day 1
you can cover Zoological garden which is beautiful place to visit for first time
Day 2
2nd day, you can cover awesome Mysore palace in morning after breakfast where you can see historical items, mesmerizing art work of palace.
Also, would suggest to cover sand art if you have sometime along with chamundeshwari temple in evening before 6PM.
You can also visit Planet Earth Aquarium if you have time.