Trivandrum is well connected part of Kerala, that be from any part of India reaching is easy. You need 2 days to explore best parts of Trivandrum. From Trivandrum Alleppey is 4 hours drive. So best picturesque are seen in Alleppey. Two days is much needed here. From Alleppey Munnar is 4 hours away. Munnar is a very popular tourist spot of Kerala with best weather and greenery now. Spending two days here you could head to Kumarakom which is 4 hours away. You need a day here and proceed towards vagamon which is 2 hours away. From vagamon you can drive back to Trivandrum. Another route you could try is from Trivandrum head towards Kochi which is 5 hours away. Spend 2 days in Kochi, then head towards Poovar which is another 5 hours ride. Spend two days and proceed towards Idukki, from here Nelliampathi is 5 hours away. From here vythiri is 6 hours drive. Since driving time is more here but spots are too beautiful up to you to decide. Every above mentioned spot needs one and half hour day to explore and other half day to travel. Mere suggestion I have given, sure there are other travellers who might guide you much better in the forum.