How many days to spend at Kanyakumari ?

Ideally one day is enough to see all the above place. But you should reach there by night, so that next day morning you can view the sunrise. Then get yourself ready as fast as possible to be ready at the ferry services by 7.45 am to see Thiruvalluvar Statue and Vivekananda Rock Memorial ,so that you will not spend much time standing in the queue(Half an hour delay will cost you 2 hrs standing in the queue,especially in weekends and that will affect your visit to other places,if you are there for one day only). And after coming from there, you can have a look at other places and come back by the evening to see the sunset.

If you plan 2 days, then you can plan in comfort for the above places and as well visit some other places or spend some time near the seashore which is quite relaxing.