Lauren, you refer to what was until 1918 the small Thuringian Duchy of Saxe-Coburg-Gotha (in German: Sachsen-Coburg-Gotha), the capital of which was the city of Gotha, the summer residence of the Duke the city of Coburg. Saxe-Coburg-Gotha covered an area only about half that of the U.S. state of Rhode Island. (Queen Victoria's husband, Prince Albert, was from Saxe-Coburg-Gotha.)
Following World War I, the various small Thuringian states consolidated to form a new state called Thuringia (in German: Thüringen), the capital of which was the city of Weimar. In 1944, the Prussian enclave of Erfurt was made part of the state of Thuringia as well and is today the capital of Thuringia. Thuringia is located almost right in the middle of Germany.
One thing I do have to mention: In 1920, the city of Coburg and environs decided not to become part of the new state of Thuringia. Coburg chose instead to become part of Bavaria. So today, the Saxe-Gotha portion of the former Duchy is part of the state of Thuringia, and the Saxe-Coburg portion of the former Duchy is part of the state of Bavaria.
Hope this helps.
Robert