They would arrange for a sight seeing. But I guess they charge extra. Maharaja is good and also there is a Hotel by name Gayatri Bhavan. Just 5-10 mins. away by auto.
You can plan like this:
1) Day 1: Mysore Palace (both day and night) and Jaganmohan palace (inside Mysore City). No need of a cab.
2) Day 2: Sangam, Nimishambha temple,...
more... Gumbaz, Daria Daulat, Gosai ghat, Srirangapatna and Ranganathittu Bird Sanctuary.
3) Day 3: Chamundi Hill, Nanjangud and Brindavan Gardens.
For day 2 and 3, I would suggest for a private cab not because of the connectivity, but only due to save the time and language issues..