Just a reminder that Tsukiji Market is closed not only on Sundays, but other days this month due to the holidays. Here is the market calendar for 2011 and 2012. Below are the days it is closed for the next four weeks.
Dec. 11, 14, 18, 23, 25 (short day), 31
January 1-4, 8-9
If you are in Tokyo only while Tsukiji is closed, the next best place to go would be to Ameyoko near Ueno and Okachimachi stations. I believe (but am not 100% sure) that it is only closed on January 1st.