Just to give you a sense of where you are.....if you've already defeated Katz and talked to Grubb and built the clockwork, he tells you that Meowiarty is in Big Ben. However once you get to the museum - I think you're told to talk to Sherlock in the Museum - you find out you have to do Counterweights East and West. THEN you get to work your way up Big Ben and finally face Meow Boy. If Baxter hasn't told you about unlocking all those doors yet, you have some things to do before you face Meowiarty.
Goodness gracious. Open your quest log file, and find the quest "Stop That Cat". Click on the Information/Dialogue Bubble in the upper left corner of the quest box. It will show you what you have done already, and what you need to do "after that".