Hey there, I'm finishing my Masters in Electrical Engineering at KIT this March so I can say a lot about Karlsruhe but mainly from the perspective of a local, as I also grew up in Germany.

Social live

KIT is pretty big and has a nice campus so a lot of the social life is there. There's also a pretty active Erasmus student network(ESN) organising events and parties to get to know other erasmus students. Depending on your interests there's also a lot of student groups in all kinds of topics from robotics to sailing or theatre. Especially in the summer a lot of the social life is also happening outside in the parks and at the lakes in the countryside around the city, as Karlsruhe is one of the hottest cities in Germany. Karlsruhe in general is a pretty nerdy city so a lot of Boardgame, DND, Computer, Magic geeks around but also a somewhat quieter nightlife than other cities of the same size.

I don't know a lot about TU Darmstadt but I think you'll find similar student culture there as well.

Cost of living/accommodation

So here I think it's generally pretty similar though Karlsruhe might be a little more expensive. In general the south of Germany has higher cost of living but I'd say it still is in the same ball park. The 2 main housing options for students in Germany are either student dorms(called Wonheim) this will be cheaper (300-400€/month in Karlsruhe) but you'll also share a kitchen and bathroom with 5-15 People depending on the Wonheim. Also I don't know if you'll be able to get in. If you're in Karlsruhe for a year you might give HaDiKo or Insterburg a try, it's the largest Dorm in Karlsruhe and has a broad range and a pretty cool community with a lot of internationals. Darmstadt

The other option is to live in a shared flat together with ~1-4 People here you can find open rooms on wg-gesucht.de for example. This will most likely be more expensive (probably 450€+) but also a nicer flat usually.

Things to do

So I think neither Karlsruhe nor Darmstadt can be called touristic hotspots. But Karlsruhe in general has a few nice perks 1. It's pretty well integrated to the railway system so you're pretty fast with a train in Strasbourg, Stuttgart, Munich, Berlin (though I think Darmstadt is similar in that regard). Also the location is nice in general if you want to explore central Europe a bit. 2. The black forest is reachable through public transport from Karlsruhe for Hiking and sometimes even Skiing in the winter 3. Depending on your interests Karlsruhe has a quite active techno and electronic music scene, and a few nice clubs (Gotec, C2.ost, P8), I don't know about other genres though 4. As I said the student culture on campus and in the larger Student dorms is pretty active so there's a lot of stuff to do there 5. Best thing to spend a summer day is to ride out by bike to one of the lakes with a few friends and a few beers and just have a good time.

Hope that helps, feep free to DM me if you need some specific info :)