In this sentence the word "but" is a coordinating word.
There are seven coordinated conjuctions which are and, but, for, nor, or, so, and yet. Coordinating conjunctions connect words, phrases, and clauses. They connect sweeping ideas together, creating cohesive, comprehensive ideas. In the case of BUT, it shows contract between the first idea and the second one. In this case the contradictions lies in the fact that the girl wanted to sit in a place where there were no more available sears.