First of all, one must realize that major combat had ceased some time before (14 August) and that the greater Tokyo area was hardly an isolated holdout fortress but a badly beaten, burnt urban ruin. It wasn't as though Japan surrendered and the next morning the Missouri sailed in--this was a planned operation, land-sea-air. What's more, the Missouri was hardly there alone. There were nine other battleships, five small carriers, and a variety of cruisers, destroyers, and other auxiliaries, which taken together dwarfed the remnants of the Japanese navy and possibly rivaled its serviceable merchant marine as well. Wikipedia, of all places, has a pretty good list of the ships in there. One thing you'll notice is a lot of landing craft, transports, and other support ships including a load of minesweepers for underwater security too.

That's because by 30 August, days before the surrender, the fleet had already landed the 4th Marine Division near Yokohama, with some British and other units securing/demilitarizing forts and the like, and so had taken effective occupation of the Tokyo Bay area. General MacArthur followed the same day. In the preceding days, they had put enormous pressure for detailed information about any minefields or hazards from the Japanese, which secured cooperation. For some maps and a nice quick rundown, the National Park Service actually has a good account online of the process of securing the area for Allied warships, entitled "Securing the Surrender," by Charles Smith. In terms of the ships' own preparation, this excerpt is telling: "At 0900 on 28 August, the first American task force, consisting of the combat elements of Task Force 31, entered Tokyo Bay and dropped anchor off Yokosuka at 1300. During the movement, Naval Task Forces 35 and 37 stood by to provide fire support if needed. Carrier planes of Task Force 38 [part of it, really, which was large and safely offshore, with 5-6 fleet carriers and several light carriers and related escorts, as this 17 August 1945 US Navy image shows -edited] conducted an air demonstration in such force 'as to discourage any treachery on the part of the enemy.' In addition, combat air patrols, direct support aircraft, and planes patrolling outlying airfields flew low over populated areas to reinforce the allied presence." They were taking no chances, and operated slowly and deliberately to secure land approaches, maintain alert at sea, and have patrols in the air.

[edit 2: noted minesweepers and pressure on Japanese to disclose mined areas]

[edit 3: in response to a PM about why an Africanist knows this, the reason is because my uncle was on CAP over Tokyo Bay at the time, so I grew up learning about the USN experience of the era. It didn't hurt that my father served on Missouri herself from 1947 to 1953. It got me into history, but we never do control where we go from there. I've still got a big soft spot for naval and maritime history, although nowhere near /u/jschooltiger 's chops...]