The Sultan Abu Baker Mosque was constructed upon a hill overlooking the Johor Straits between 1892 and 1900 and is the state mosque for Johor. The mosque can accommodate 3,000 worshippers.
I recommended taking a short trip to visit and walking around the grounds. You can walk to old town from without much trouble (I would guess it is less than 2 km from old town), obviously you can drive or take a taxi if you prefer.