For Stuttgart:
excellent museums including trhe Mercedes Benz and Porsche ones, after all, Stuttgart is where the automobile was invented
excellent opera and world-famous ballet
three large mineral baths associated with western Europe's largest mineral waters
the world's first modern TV tower has an observation deck
the tourist office has a map for 0.50 that has a nice 1-3 hour walking tour of central Stuttgart
Stuttgart is the largest city in Germany with vineyards, and they are a rarity for a large city in Germany being so extensive, there are panoramic walks through them with wineries and palaces to eat along the way ( http://www.stuttgarter-weinwanderweg.de )
http://www.wilhelma.de Europe's largest combination zoo-botanical garden set amidst the nice Moorish architecture of this former palace
There are many other things to see and do.
Some websites for a few of our favorite places around Stuttgart:
http://www.esslingen.de Esslingen with its well preserved medieval center
http://www.ludwigsburg.de Ludwigsburg with Germany's largest perfectly preserved Baroque palace (in http://www.schloesser-und-gaerten.de ), the Swabian Versailles with the longest and best palace tour that I have been on in Europe (several days to see everything there)
http://www.tuebingen.de Tuebingen our favorite town to repeatedly visit in Germany with its hilly cobblestone streets, half-timbered houses, castle, and interesting nontourist shops
http://www.schloesser-und-gaerten.de well-preserved medieval Bebenhausen Monastery just north of Tuebingen
http://www.burg-hohenzollern.com fairytale-like Hohenzollern Castle by Hechingen
http://www.schloss-lichtenstein.de fairytale-like Lichtenstein Castle east of Reutlingen where about a month of go they finished shooting Sleeping Beauty
http://www.schloesser-und-gaerten.de Hohenneuffen, the largest castle (fortress) ruin of the Swabian Alb
http://www.gestuet-marbach.de Germany's oldest state stables at Marbach (Gomadingen) where you can visit the stallions in their stalls and the mares and colts will be out in the fields
http://www.schwaebischealb.de Swabian Alb, low mountains wiuth lots of castles and caves including the 3 mentioned above and the stables, and excellent cliffside scenery
http://www.schwarzwald-tourismus.info Black Forest
All are within an hour or a little more from Stuttgart.
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