It’s fun and it’s cheap. Rent will cost you ~200–300 EUR if you want to have a decent room, 400–500 for a 3 rooms apartment. These are prices for the city center, it’ cheaper in the outskirts.
There are so many events, culture, sports, everything, that you will easily be able to do something different every night. To Berlin, it’s 2 hours by car or one hour by train.
Oh, and nature is great, rivers and lakes for swimming and canoeing, woodland and hills for hiking and cycling.
Leipzig is big enough a city to offer something for anybody, and small enough to get anywhere within max. 45 minutes.
Seriously, I think it’s the best city in Germany to live in. I know few people who have been living here and don’t share this opinion.