Places to visit in Stuttgart are
Wilhelma Zoo: Wilhelma is not a Zoo in the generally accepted sense of the word - it's the only zoological botanical garden in Europe.And with its combination of plants, animals and historic buildings unique worldwide. From HauptBahnHof take U14 towards Remseck and get down at Wilhelma stop. Ticket costs aroun 12 EUR in summer and 8 EUR in winter. Be there around 9 Am it takes full day. As soon you enter in to the zoo you will find maps just plan which all things to cover and go according to that. Must visit place in Stuttgart & worth too.
TV Tower: The Fernsehturm Stuttgart (TV Tower Stuttgart) is the world's first TV tower built from concrete and prototype for many towers over the world. From HauptBahnHof take U7 and get down at Rubank Fernsehturm. Ticket for getting top of the TV Tower costs around 5 EUR. From top you will have fantastic view of Stuttgart and Gazi Stadium.
Benz Museum: The Mercedes- Benz Museum is an automotive museum. Stuttgart is home to Mercedes-Benz brand.Take U2 from HauptBahnHof and get down at Mercedes Strasse. Ticket costs around 8 EUR. From 4 pm it costs around 4EUR.
Porsche Museum: This is also an automotive museum of Porsche. Take U15 from Hauptbahnhof and get down at Salzwienenstrasse from there it is just 4m. Ticket costs around 8 EUR.
Ludwigsburg: Ludwigsburg Palace is a historical building in Ludwigsburg. It is one of the country's largest Baroque palaces and features an enormous garden in that style. Take S4(Direction Marbach) from HauptBhanHof and get down at Ludwigsburg stop form there take Bus 421 direction Neckarweih.Hohenrainstr. Entrance ticket cost around 6.50 EUR per person. Group of 20 5.80 EUR.
Max Eyth See: Max Eyth see lake in Stuttgart is an artificial lake on Neckar. In summer you can do boating and BBQ day over there. In winter lake is fully frozen you can do skating and it is totally a diffrent experience. Beautiful place to visit in both Summer and winter.