Basically, all located around the Market (Palace) Square: former City Palace, The Old Town Hall (1608-1610), New Town Hall (1905) and the Protestant Market Church (1853-1862). In August, the wine festival is held here.
The most famous building in the city is Casino. It is widely known after the novel Player (1866) by Dostoevsky who played here many times. One of the halls is named after him.
Resort Park is located behind the casino.
There are also few small parks in the city center.
Main train station
Typical urban development
Villa in the old town
Curious showcase
Old fire hydrant
In 4 km from the train station, on the banks of the Rhine, there is another point of interest, Biebrich Palace (google.maps). The former princely residence was built in 1700-1750. There is no free access inside, but you can walk in the park. We got there on foot, but you can use bus (http://bahn.de) to the stop Biebrich Schloß, Wiesbaden.
Getting there: By train to Wiesbaden Hbf, use bahn.de, the nearest large city is Frankfurt.