Visiting mysore on Saturday... Any advices would be appreciated

So I[M22] and some of my friends are visiting mysore on this Saturday or I should say we are already here in mysore for our internship in a well-known company... But we are going out on saturday because we are not supposed to go out on weekdays... We know only one place and that is the palace. I would really appreciate if you guys would add more places that would be fun. And transport I should consider, like autos or govt buses... We have females in our gang too... So any places that we should avoid... Anything would be great