KanyaKumari

KanyaKumari is the southern tip of India.

Places to see:

Vivekananda Rock Memorial and Tiruvalluvar statue
KanyaKumari Temple
Gandhi Mandapam, Triveni Sangam, Sunset
Vivekananda Kendra for Sunrise, sunset point in private beach and museums about Vivekananda's teaching.

Places to visit in Kanyakumari/Nagercoil district

Suchindram Temple - Very famous temple.
Nagaraja Temple
Tiruparuppu Falls - I think this is an artificial falls created from the Neyyar river through a dam. Very nice and enjoyable.
Hanging Bridge - Old bridge which is one of the highest bridges, offers very scenic view.
Padmanaba Palace (This is different from Padmanabha swamy temple and palace in trivendrum) - Open till 5 pm.

How to reach:

Kanyakumari has a railway station and bus stand.
By train, you can reach Nagercoil or Kanyakumari itself. Autos, Taxis or buses are available from NagerCoil to Kanyakumari.

Accomodation in kanyakumari

Lots of hotels available for reasonable rates. All the places to visit are in the radius of one kilometer. So you can book any hotel close to Kanyakumari junction.
https://www.google.co.in/maps/search/hotels+near+Kanyakumari,+Tamil+Nadu/@8.086789,77.5458705,15z/data=!3m1!4b1

Eating options

Not much eating options in Kanyakumari for the Vegetarians. Canteen @ Vivekananda kendra is decent. There are couple of restaurants in the main road. For non vegetarians, there are plenty of restaurants near the main kanyakumari junction.

Time to take to see all places

It takes 2 days to see all places patiently. But you can squeeze it to one day as well.

Vivekananda Rock memorial - There is a boat service from main Kanyakumari junction. This may be crowded. Ticket is around Rs. 60/-. This may be crowded during holidays. Also boat service depends on weather conditions.
Kanyakumari temple, gandhi mandapam, Triveni Sangam, sunset - You can cover all these in one evening.
Vivekananda Kendra - For the spiritually inclined only. There are very reasonable accomodations available as well. Vivekananda museum and the private beach are the main attractions.

Trivendrum

Trivendrum is the capital of Kerala and is located to the south of Kerala.

Places to see in Trivendrum and around Trivendru

Trivendrum City - Kovalam Beach, Padmanabha Swamy Temple and attached Palace museum, Zoo, Museum, Art Gallery
Veli tourist village, Shangumugam beach, Poovar backwaters, Vadakayal Beach.
Neyyar dam, Ponmudi hillstation

Time to see the places

It takes around 3 days to see all places.

Accomodation

Hotels like Chaitram, etc are available close to Main bus stand and Trivandrum Central Railway station. KTDC has regular daily packages to all places of interest.
https://www.google.co.in/maps/search/hotels+near+trivandrum+central/@8.4861845,76.9506843,17z

Eating Options

Good Vegetarian hotels are available near Bus stand/Railway station. Hotel Aryaas also called Arya Nivas Restaurant near Hotel Chaitram, Restaurant @ Hotel Chaitram, India Coffee house next to bus stand are all decent options.