2 places I recommend
These are the two restaurants in Leipzig I have eaten at myself and would recommend.
A restaurant in the courtyard of the Städtisches Kaufhaus in Leipzig, a 1901 building on the site of the city's medieval cloth hall, cooking seasonal food from regional producers. The setting wasn't particularly pleasant — it felt a bit like eating in a museum hallway — but the food was good.
Address: Innenhof Städtisches Kaufhaus, Neumarkt 9, 04109 Leipzig, Germany
A branch of the Italian chain on Martin-Luther-Ring in Leipzig, whose 45 cm pizzas are made deliberately wider than the plates they arrive on. Nice casual place for pizza or pasta. It's decent, and honestly in Leipzig it was a challenge to find restaurants that were exceptional.
Address: Martin-Luther-Ring 12, 04109 Leipzig, Germany