Well. You don't have to necessarily stay in each of the places you have mentioned.
In Chennai (Madras), you have Mylapore Kapaleeswarar Temple. If you have Chennai as your base, you can cover Kalahasti, Kanchipuram and Thiruvannamalai. You can then move (by road) to Thanjavur/Kumbakonam via Chidambaram. From that base, you can visit Navagra sthala (which are indeed Siva temples). You can then travel, again by road, to Tiruchi to visit temples there. Then to Madurai, yet again by road. You can take a day's trip to Rameswaram from Madurai. You may consider visiting "arupadaiveedu" of Lord Muruga with Madurai as your base. Otherwise, you may visit the "arupadai veedu temple" in Chennai.
Madurai is closer to Sri Lanka as well, though I am not sure of the mode of travel. There are flights from Chennai to Colombo.
Kerala is nearer from Madurai. You can either fly or travel by train to Kochi or Thiruvanathapuram. You can cover the temples in Kerala by road. You can fly back to Bengaluru (Bangalore).
For temples in South Karnataka (Sringeri, Kollur, Horanadu Annapoorneswari, Dharmasthala Manjunatha Swamy, Udupi Krishna, Kukke Subrahmanya, Murudeeshwar), you can hire a raxi from Bangalore and check in at hotels as is necessary.
As for the costs, it depends upon your choice. A decent stay would cost you about $50 a night and a decent meal would cost you about $5 per person. Taxi would cost you about a Dollar for a distance of 3 K.M. Beware of touts and cheats. They are galore at tourist places. Try to be as much "Indian" as possible. It would keep those people off from you.
Hope it helps.
P.S.: Why don't you fly via Johannesburg and take me with you? I would be a good guide since I know all these places and I know Tamil very well.:crazy: