If you want to get the tactical situation, I suggest:
http://belmontclub.blogspot.com/
They seem to have good insight. I don't know where or how they get it, but it seems to be borne out in practice.
My synopsis:
Our guys appear to have surrounded the city first, then took the bridges and hospital in the west on the river. British troops and others are in a blocking position there. Then we controlled the road east-->west possibly by air while our guys swept down from North-->South, in some type of pattern that seems to have created pockets of isolated terrorists wherever they decided to camp out. Those who ran have been herded Southward and Westward , being pinned against that central road and the River. That killing box is getting smaller and smaller as we advance now, and the terrorists are having a choice of trying to run and get killed on the road by Americans or by the British on the River, or they can themselves become an isolated pocket to be dealt with later.
Our technology has stood us in good stead, as the killing ratio appears to be on the order of 100:1 in our favor despite the great advantage of the terrorists having been dug in and setting bombs and booby traps galore. Mosques that the terrorists fire from have been targeted by our artillery and aircraft. Those that have become hideout/sanctuary are being stormed by the Iraqi forces.
Sounds like not much has been done in the Southwest quarter of the city, but it was not considered a hot spot, I guess... more attention was paid to the Southeast "industrial" part due to potentials but again wasn't the major area of action.