I went on a course in Jena recently and was very happy to discover this cafe (and the Biomarkt next door) on HappyCow.
It is a cheerful cafe which is attached to a fair trade clothes shop. You can sit inside or on the pavement (it's a quiet street).
There is a limited choice of food - soup and cupcakes basically, and pizza on Saturday, but it is nicely prepared and served on interesting shaped crockery :-) They publish the list of soups for each day of the week on their Facebook page.
I went a couple of times with people from my course. The first time the soup was very good - the omnivores I was with were impressed. The second time we arrived a little late and the soup had run out. The cupcake I had instead was fine but if you want soup it might be a good idea to get there earlyish.
I also went back with my partner on the Saturday and sampled the pizzas, which were served cold (not sure this is usual - I may have missed an explanation!) but were tasty just the same.
The staff are very friendly and will speak German or English, whichever you prefer. It is near the university and town centre and round the corner from the Schwarzer Baer hotel.
I believe the food is completely vegan but I'm not sure about the drinks - one of the omnivores thought she had cow milk in her coffee, but I didn't check.
Cons: Only open in the daytime I think