I strongly recommend the book Computational Complexity: A Modern Approach by Arora and Barak. When I took computational complexity at my Master level, the main textbook is Computational Complexity by Papadimitriou. But, maybe due to my background in Software Engineering, I found the writing in Papadimitriou challenging at times. Whenever I had problem understanding Papadimitriou's book, I simply went back to Sipser, or read the draft of Arora and Barak.
In retrospect, I really like Papadimitriou's book, and I often find myself looking up from this book. His book has plenty of exercises that are quite effective at connecting readers to research-level questions and open problems.
In any case, you should have a look at both Papadimitriou and Arora-Barak. People also suggest Oded Goldreich's textbook, but I really prefer the organization of Arora-Barak.