Things like the blue and green lake can be accessed without the need to join a tour. As is most of the stuff in Rotorua actually. As for getting around Rotorua,,,I am still working on that one for you. I always had my own car there so it was not an issue for me.
The wai o tapu reserve would probably be the furtherest away from Rotorua but most of the other things are within the Rotorua city boundaries.
Hi, The site you want is
Check the sightseeing, and tours and day trips.
I guess you are arriving at Auckland Airport, so there are taxis and shuttles to take you into Auckland city.
Travewl from Auckland to Rotorua,try
www.intercitycoach.co.nz or www.newmanscoach.co.nz
I know intercity goes there, but not sure about newmans (haven't travelled by bus for a long time)
Hope this helps a little.