To get here from Trivandrum, first take a bus heading to Kanyakumari and get off at a place called Thuckalay (Rs24). Then take an auto-rickshaw from the small bus station to the palace (which cost me Rs20). I then took an auto-rickshaw back to the bus station in Thuckalay and caught another bus to Kanyakumari (Rs10.50). Don't worry about bags as you can deposit them at the palace ticket counter.
I went to Padmanabhapuram way back in October, 2003. I must say, I am very good at bargaining. We took a car on rent (Ambassador car), me, my mom and dad. Since this is a BIG car, we sat comfortably. For Rs. 650/- in total, we went first from Kanniyakumari to Suchindram (where the famous Brahma, Vishnu and Shiva trinity temple is situated), then to Nagercoil (where the Nagaraja temple is situated), then to Padmanabhapuram, then to Vizhinjam (having a very good Aquarium), then Kovalam (the famous beach), then Trivandrum (Thiruananthapuram) and again back to Kanniyakumari via Padmanabhapuram again to see the view of the palace during the setting sun. we set off at 6 AM and returned at 9 PM.