Historically, large urban battles have always been part of a larger campaign. Stalingrad from the German perspective was part of the general offensive whose goal was to destroy the Soviet Union. From the Soviet point of view Stalingrad represented a sinkhole which would empty the German 6th Army of its combat power preparatory to its later encirclement. The Battle of Manila was largely fought the possession of the seaport, which the Japanese wished to deny to American logisticians.
The relatively recent Battle of Grozny also had a wider context. Parameters noted that the Chechens saw it as part of their politico-military strategy for wearing down Russia. Grozny was merely the first in a succession of via Dolorosas they wanted to present the Russians.
The Chechens reverted to a battle of "successive cities" after the Grozny battle ended, hoping to recreate their Grozny successes elsewhere. They moved their operations base to Shali, Argun, and other city centers. They recognized that they could accomplish two things with this tactic: they could negate Russian advantages of firepower in the open from helicopters, fixed-wing aircraft, and tanks, and they could blend in with the local population to their advantage. This not only continued to make it difficult to distinguish combatants from civilians, but it also helped the Chechens get the local population on their side. This was usually the result when Russian forces entered a city, destroyed property and buildings, and killed or wounded civilians while searching for their armed opponent.
The Israeli Battle for Beirut was also part of a larger campaign named Peace for Galilee whose goal was to destroy a mini-PLO state that had fastened itself onto the carcass of a fragmented Lebanon. Wikipedia summarizes the situuation then.
In 1981, armed forces of the Palestine Liberation Organization (PLO) occupied large areas of southern Lebanon. Attacks against Israeli territory increased, as the PLO's armed forces used Lebanon as a base to attack Israel with rockets and artillery. PLO soldiers fought with Lebanese forces; in 1996, the World Lebanese Organization, the World Maronite Union, and multiple human rights groups concerned with the Middle East issued a public declaration accusing the PLO of genocide in Lebanon and stating they were responsible for the deaths of 100,000 Lebanese civilians. Due to ongoing civil war since 1975, Lebanon had no effective central government at the time.
But from the first, the Israeli cabinet was uncertain about how hard or fast to move. As a result, they never trapped the elements they intended to destroy.
Suspicious of Sharon’s sincerity and concerned about possible Syrian intervention, the cabinet decided to monitor the campaign closely, thus leaving any military escalation subject to its approval. Begin told the ministers that “the cabinet will meet daily and make decisions according to the evolving situation.” ... In the five days that followed Begin’s announcement of 8 June, Sharon did everything he could to gain approval for tactical moves that inched the IDF to an encirclement of Beirut. The resultant piecemeal movements aggravated the question in the IDF concerning the final objectives of the campaign. Meanwhile, confusion started to grow in both the cabinet and the public when military operations began to exceed the publicly stated forty-kilometer limit.
Apparently at this juncture in the war, the IDF missed a golden opportunity to capture west Beirut in quick order. A Western reporter inside Beirut at the time observed how “the sheer speed and depth of the mass Israeli invasion stunned both the Palestinians and the Syrians.” In interviews conducted after the war, a number of Palestinians depicted the Arab forces in the city as “demoralized, dispirited, and panic-stricken as a result of the crushing defeat they had suffered in the previous week.” ...
In response to Sharon’s encirclement of Beirut, the Israeli cabinet changed the objectives of Operation Peace for Galilee. Instead of placing the civilian population of Galilee out of artillery range, Israel now demanded the departure of all Palestinian fighters and Syrian troops from Beirut. The Lebanese Army would enter west Beirut to accept arms from the PLO fighters, who in turn would leave without their weapons.
Arafat rejected Israel’s demand to leave the city with his organization and decided to bide his time. Meanwhile, Arab forces in west Beirut took advantage of the Israeli delay in assaulting the city by frantically fortifying their own positions. “They mined the southern approaches to the city, booby-trapped junctions, placed explosives in buildings so that they could be blown up to collapse on advancing forces, dug trenches, and fortified bunkers.” Eventually, a system of strong points and barricades guarded all possible avenues of entry into the city.
The Israelis eventually won the urban battle from a military point of view, but were counterattacked politically. The Israeli Labor party called for an end to the war. The Reagan Administration attempted to negotiate an omnibus withdrawal of all parties: the Syrians, the PLO and the Israelis. America backed its guarantee with Marine peacekeepers, of whom 220 were killed in a suicide bombing of their barracks. (Answer the trivia question: the most costly US urban battle in the Middle East is a) Beirut, b) Baghdad, c) Fallujah, d) Mogadishu. Bonus question: which were UN missions?) Although Israel withdrew nearly completely from Lebanon under the deal, the Syrians never did. Wikipedia again:
On May 22, 2000, Israel completed its withdrawal from the south of Lebanon in accordance with UN Security Council Resolution 425. A 50 square kilometer piece of disputed mountain terrain, commonly referred to as the Shebaa Farms, remains under the control of Israel. The UN has certified Israel's pullout and regards the Shebaa Farms as occupied Syrian territory ... During Lebanon's civil war, Syria's troop deployment in Lebanon was legitimized by the Lebanese Parliament in the Taif Agreement, and supported by the Arab League. Fifteen years later, Damascus justifies its continued military presence in Lebanon by citing the continued weakness of the LAF (Lebanese Armed Forces), Beirut's requests, and the agreement with the Lebanese Government to implement all of the constitutional reforms in the Taif Agreement. Contrary to Taif, the Hezbollah militia has not been dismantled, and the LAF has not been allowed to deploy along the border with Israel, though it was called on to do so by UN Security Council Resolution 1391, urged by UN Resolution UN Security Council Resolution 1496, and demanded by UN Security Council Resolution 1559.
An estimated 20,000 Syrian troops (down from 35,000) remain in position in many areas of Lebanon, although Taif stipulations called for agreement between the Syrian and Lebanese Governments on their redeployment by September 1992. ... Syria has been accused of turning Lebanon's Government into a puppet. Recently, the US has begun applying pressure on Syria to end its occupation and cease interfering with internal Lebanese matters. ...France, Germany and Britain, along with Lebanese politicians have joined the US in denouncing Syria's interference. On September 2nd 2004 the UN Security Council adopted UN Security Council Resolution 1559, authored by France and the US in an uncommon show of cooperation. Echoing the Taif Agreement the resolution "calls upon all remaining foreign forces to withdraw from Lebanon" and " for the disbanding and disarmament of all Lebanese and non-Lebanese militias".
Although Israel "won" the Battle of Beirut and the Russians eventually ousted the Chechens from Grozny, they achieved far less than they bargained for. These two instances illustrate how Islamic strategists believe it is possible to lose a battle, yet win the campaign of "successive cities" within the wider war. By skillfully playing on the political divisions of their enemies and "internationalizing" a conflict they may be able to politically retain objectives that they could not defend by military means.