I agree with many of the reviewers below - this place is truly in need of some sort of rejuvenation. I went to Kota on a Sunday and it was extremely packed, with many Jakartans crowded in the square to watch some street performances and the like. Many street vendors selling all sorts of knick-knacks were also there. Cafe Batavia is not bad - the 2nd storey has a good view of the square below, and of the history museum; the restored Dutch building it's housed in is also very nice.
But what is more depressing is the general state of neglect that seems to have befallen this area. Just right next to the restored Cafe Batavia is a neglected old building that has half its roof caved in - in fact, all around the square buildings that could have looked very nice ages ago have all decayed and fallen to bits. Interested to see if there were any other notable sights, I even crossed the canal (which is also not the most aromatic nor most pleasant one around) to have a look, but the general condition of the buildings together with their seeming abandoned condition made me do a double-take.
Having said that, there are some very nice sights to see - the history museum, Cafe Batavia, Pos Indonesia, Bank Indonesia and Kota train station are all very nicely restored, but other than that the general neglect is quite depressing. I hear there's a plan to refurbish many of the colonial-era structures - if so, that would be a great shot in the arm for this place.