The excellent Gewandhaus Orchestra performs both in its own hall (of the same name) and also (at times) in the pit for performances of the Oper Leipzig. The Gewandhaus hall and the Oper (both replacing structures destroyed in WW II) are across from each other in Augustusplatz, just a few blocks from the Hauptbahnhof and the old center city. Prices are very reasonable, especially considering the very high quality (especially when music director Riccardo Chailly is on the podium).
Speaking of the Hbf, there is a very large multi-level shopping mall on the two levels below the train platform area. It has a wide variety of shops and eating places.