If you want to do a day trip from Karlsruhe, Heidelberg, Stuttgart, Freiburg and Strasbourg (France) are great options close by.

Due to time constrain, we decided to go Heidelberg. We took train from Karlsruhe Hbf to Heidelberg Hbf. It took us less than an hour and cost less than €20. You can purchase your train ticket from BAHN website. You need to print out your e-ticket and bring the credit card you used to purchase your train ticket for verification.