Falco and Stadtpfeiffer are the classic touristic restaurants!!! I lived in LEJ for half a year and loved it!
Visit "Die Drogerie" you can go there from the center of the city by tram, I´m not sure which line, but I think the Number 4 (station Menckestr.). Daily changing Menu, very good open wines, and Leipzig is relatively cheap.
I just found it on the Net: Tel: 0341 - 5906309
You will need a reservation. A very good Greek in a wonderfull old house, is across the street!
Leipzig is not the heaven of great dining in Germany. Like the rest of former DGR it still suffers the drought of fifty years suppression of private enterprise, a key of success in culinary creativity. Dresden progessed more rapidly, by the way.
This in mind, you may find some decent places for good meals.
The "Falco" in the 27. floor of Hotel Best Western was praised this month in Feinschmecker magazin as "Resto of the Year", whtever that may mean.
I had a rather decent meal in July in Historische Weinstuben in Auerbachs Keller.
They also offer more popular chow in a wine/beer celler adjacent in the same location.
Stadtpfeiffer has been mentioned as a deecent place.
Don't miss the many Cafe's and local places, just for the fun.
I hope this helps to enjoy a stay in this historical - though heavily bombed and destoyed
Hope this helps to en