Help needed! Trip-Advise

Hey guys! I hope to get some advice to plan my further trip. It’s my first time in India & Kerala. Currently in Kochi since more than 2 weeks and we plan to head further on the 6. January. Love the vibe and the people here! So friendly ❤️🥰 We have a 3 month-visa and want to stay until india kicks us out. So 2 more month. The last month we planned to stay in Andaman Islands. So a flight from Kochi/Bengaluru/Kochi. My plan in southindia was to head south to Backwaters and some Beachplaces. Afterwards rent a car from Indusgo and heading inwards. We don‘t know yet if we will give it back at kochi/Bengaluru/chennai. That‘s why i‘m asking for advice. The trip south seems good (also appreciate some more tips or feedback). I‘m not sure if its the best to rent a car. What are you guys thinking? We don‘t have something we want to see. We were in SriLanka and Maledives before and i‘m from Switzerland. So neither beaches and also mountain-areas wouldn‘t impress much. So just nice places for a hike/ views / chill / have a good time / less tourists Thanks in advance for help! My plan: Kochi Allapuzha by Train Kollam by Ship Varkala by publicTransport Poovar by publicTransport Thrivandrum by PublicTransport Rent a car - Roadtrip: Vagamon Thekkady Munnar Kollukumalai Kodaikanal Maybe Athirappilly Udhagamandalam Maybe a nationalpark Mysuru Maybe Bengaluru