You can find different modes of transportation including information on costs and how to purchase tickets or make bookings on the Rome2Rio website. https://www.rome2rio.com/s/Frankfurt-am-Main/Wiesbaden
Please find here a selection of weblinks and useful information that may help you to have an even more interesting and good time while in Wiesbaden. Why not add a couple of days for exploring the city and its surroundings?
From Frankfurt to Wiesbaden
Explore the Rheingau region
Wiebaden is also the gateway to the Rheingau ("Rhine District"), one of Germany’s most important wine regions. If you are interested in visiting one of the selected wineyards, please visit the Rheingau website on https://www.rheingau.com/en for inspiration.
Städel Museum Frankfurt
A museum of world stature with an outstanding quality of the collection and high level of activity in the areas of research, exhibitions and education. The Städel moreover stands for the broad-scale involvement of the public, a factor of fundamental significance for the preservation and development of this cultural institution. For detailed information on tickets, exhibitions and further details, please visit the Städel Museum´s website on https://www.staedelmuseum.de/en.
Goethe Haus Frankfurt
In the unique atmosphere of the originally furnished rooms, the family life of the Goethes and 18th century Frankfurt comes alive. To learn more, please visit the website of the Goethe Haus https://frankfurter-goethe-haus.de/en/
Museum of Wiesbaden
Exhibitions in the Museum of Wiesbaden are organised in collections of Old Masters, Classical Modern Times, Modern Art and Contemporary Arts as well as the Natural-historic collections The museum was build according to the plans of architect Theodor Fischer in the years 1912 to 1920, and after a renovation in May 2013 presents its collections on an area of 7,000 sqm which seeks to esthetically combine the contemplation of art and nature. Please visit the website https://museum-wiesbaden.de/en/ for the calender of events and exhibitions as well as tickets and opening hours.
The church is located on Neroberg and is called the Greek Chapel by local residents. Duke Adolph von Nassau had the church built between 1849 and 1855 to house the funerary monument of his wife, the Russian Princess Elisabeth Michailowna, Grand Duchess of Russia and Duchess of Nassau. The Nassau Master Builder Philipp Hoffmann erected the house of prayer following the model of the Moscow Church of the Redeemer in the style of romantic Historicism.
Since 1859, Germany´s first Austrian coffee house is an exclusive meeting point for inhabitants and visitors of Wiesbaden alike. Enjoy a typical "Apfelstrudel" or a delicious piece of one of the hand-baked fancy cakes alongside your coffee or tea. This coffee place is very well frequented on the weekends, and it is recommended to make a reservation before noon. Please visit their website https://maldaner1859.de/