Grant mentions in his memoirs during the Battle of Monterrey (I don't remember the name sorry) one commander leading his men through the buildings (rather than the streets presumably) and incurring significantly less casualties.
With the prevalence of firearms and increasing urbanisation from 1700 onwards were any firm military doctrines set down on how to fight in urban areas? And how do they reflect on what is used today?
Yes, actually, in the British army during the Revolution a new form of urban fighting called 'Street firing' had been developed. It consisted of a rank of men in line firing, and switching out the front lines. The first line would fire a volley, step aside and let the line behind move on up and fire their volley, while the front line would move to the back and reload. This kind of street fighting was optimal in the days where soldiers were equipped with something like the 'Brown Bess' musket where you only had to aim in a general direction and pull the trigger. Fighting in this fashion was also optimal for retreating aggressively down a, for example, London street, but when it was in use during the Lexington/Concord battle of 1775, it failed quite miserably. It was originally meant to be put in use in tight quarters, like I said earlier, while for instance retreating through a city or a narrow street, but when it was put in use by Captain Walter Laurie of the British Army, his forces were surrounded by open plains, and not by buildings. On top of this, the Infantry that Laurie commanded, didn't fully understand the tactic, and confusion followed quickly. Since Laurie (Exactly like the incident with the American Militia earlier in the day) hadn't actually given an order to fire, when a musket suddenly went off, whoever was in line to fire, did so, assuming the order to fire had been given already. But they didn't bother retreating to the back to follow the tactic. The Americans fired in return, and routed the British who ran for Lexington and collapsed as soon as they arrived, and they were finally allowed some rest after a rather long, and taxing day, of fighting - The long day filled with fighting and marching might also explain away whoever fired the first shot.
The French in the Austerlitz campaign used a strongpoint tactic - but I'm unaware if this was doctrine or a inspiration.
At Haslach-Junigingen, Dupont put the grenadiers of his division into a fortified church and then put out skirmishers at the village edge. When the Austrian columns attacked, they were drawn into the village and where they were confronted by the fortified redoubt. The Austrians then began attacking it while the French reserve, held outside of the town, then advanced, blocked the exits and counter-attacked, routing the Austrians.
The Austrians then sent more columns and the French reset the trap several times.