Can I take my language course in a different state after getting accepted to a Studienkolleg?

Not automatically: after a Studienkolleg acceptance, going to any language school in another Land is not covered by the purpose of your residence permit by default. The permit is valid throughout Germany but tied to its purpose, so check with the Ausländerbehörde (or the German mission if you are still at the visa stage) before you change anything.

#What the law says (§ 16b AufenthG)

• The study purpose includes preparatory measures: a Studienkolleg, provided your acceptance is proven.
• A preparatory language course counts only if you have been admitted to full-time study and that admission is conditional on the course.
• The law does not tie a Studienkolleg to a particular Land, but a language school unrelated to your admission does not fall under this.

#Residence permit

A residence title is issued for the whole federal territory, yet it can carry conditions (Auflagen). If a requirement essential to it lapses, its validity can be shortened.

#Switching Studienkolleg

According to the KMK, moving from one Studienkolleg to another is as a rule not possible. A passed Feststellungsprüfung, on the other hand, is recognised by the Länder mutually. An FSP from an FH-Studienkolleg does not open access to universities.

Source: § 16b AufenthG · KMK Rahmenordnung · Conditional admission and visa