For a city with a reputation as an industrial centre Chemnitz has surprisingly many parks and gardens. Just on the northern end of the city centre is the Schlossteich (lake below the former castle) with a nice park, a half mile farther north is the large Küchwald park with several typical attractions for kids/families, tennis courts etc.
Along the Chemnitz river, from southeast through the centre to northeast, is a designed green area, sometimes wider (like at the Stadtpark in the southwest) and sometimes narrower (like north of the centre).
Close to the residential district Sonnenberg is the Zeisig forest with walking paths and a natural public bath. In the northwestern outskirts of the city is the Rabenstein Forest with a nice castle, pond, hotel and many hiking paths.
Very beautiful is the Baroque garden of Schloss Lichtenwalde, a few miles east of Chemnitz and not to miss.
Naturally, a visitor of a German city heads to the city centre first, hoping to find a cute old town. You're out of luck in Chemnitz. The old town was destroyed in WWII, not much is left. Only a few public buildings like churches, a couple of townhouses, art museum and opera house were reconstructed. The town hall was one of the few buildings that had only little damage.
So, the communists cleaned the city centre up and built large blocks in the usual post-war style. Not overly attractive in general, granted. However, if you have a closer look you can find some interesting examples of the architecture of that era and learn a thing or two.
Since the old structures were gone the architects were able to construct large blocks/structures, wide and straight streets and relatively many green areas with flower beds and trees. The overall impression is that it is much more airy and open than the typical old town of a German city (see Dresden also). One ensemble is particularly notworthy: the Stadthalle with the high-rise hotel "Mercure".
Later in the 1970s the communist administration and architects realised that people wanted smaller structures - so the designed the "Rosenhof", a pedestrian zone with shops and restaurants/cafes on the ground floor, apartments on floors above. Flower beds, fountains and benches give it a nice touch, make it a place where you actually like to spend time.
In the 1990s the large, not yet overbuilt lots in the city centre were perfect for well-known architects to construct new buildings in contemporary style, often shopping malls. Thus you find works of architects like Helmut Jahn and Hans Kollhoff in Chemnitz.
Fondest memory: Step by step the old town gets a structure back. Shopping and dining opportunities are already surprisingly good. The Markt square in front of the town hall is again the lively centre of the city, the pedestrian zone around it is quite large and a good place for people watching.
Do not miss to venture out farther north toward Theaterplatz - a very nice square with an architectural ensemble from the turn of the 19th/20th century.