Sree padmanabhaswami Temple
Attukal Temple
Napier Museum /Govt Art Museum
Kuthiramalika
Kanakakkunnu palace
Zoological gardens
Veli tourist village(10km)
Kovalam(13km from centre) and sankhumukham beach(10km)
peppara wild life sanctuary and dam (39km)
Neyyar Dam wildlife sanctuary(almost 30 km from railway station)
Koyikal palace museum (about 15 km)monday holiday as of my knowledge
Ponmudi Hill station (56 km)
Must visit Kovalam Beach. Enjoy beautiful scene and waves and can take rest on shacks.
Also can visit Lighthouse nearby which gives you full view of the city.