Keep in mind that the original objectives of Barbarossa never included the seizure of 'prestige cities' [edit: as initial goals]. Hitler didn't place great value in Moscow and that of Leningrad was tied to control of the Baltics and the northern industrial region. Instead the key aim of Barbarossa was the destruction of the Soviet Army in the border areas. This would then be followed by the occupation of key economic assets (particularly in the south), with seizure of the major cities a distant third priority.

The relevant Fuhrer Directive makes this clear:

The southern of these two army groups - in the center of the whole front - will have the task of breaking out the area around and to the north of Warsaw with exceptionally strong armor and motorized formations and of destroying the enemy forces in White Russia. This will create a situation which will enable strong formations of mobile troops to swing north; such formations will then cooperate with the northern army group - advancing from East Prussia in the general direction of Leningrad - in destroying the enemy forces in the area of the Baltic states. Only after the accomplishment of these offensive operations, which must be followed by the capture of Leningrad and Kronstadt, are further offensive operations to be initiates with the objective of occupying the important center of communications and of armament production, Moscow.

Only a surprisingly rapid collapse of the Russian ability to resist could justify an attempt to achieve both objectives simultaneously.

... Once the battle south or north of the Pripet Marshes have been fought, the pursuit is to be undertaken with the following objectives:

In the south the rapid occupation of the economically important Donetz Basin, in the north the speedy capture of Moscow. This city is a political and economical center, and is a main railway junction point

Again: the focus was on destroying the opposition armies in the field, thus precipitating the rapid collapse of the Soviet state. The seizure of the cities was the end point of such a campaign, part of the pursuit phase, and something to be conducted after victory in the field had been secured.

It wasn't until August 1941 that Hitler began to listen to his generals on the subject of Moscow. With it becoming increasingly apparent that the war would not be over that year, seizure of the city took on new importance - depriving the Soviets of a transport and communications hub. Even then Hitler resisted calls to focus on the capital, maintaining the importance of crushing Soviet armies in the field and seizing economic assets.

Sources: Chris Bellamy, Absolute War; Adam Tooze, Wages of Destruction; Ian Kerhsaw, Hitler; David Glantz, When Titans Clashed

Hitler organized a three-pronged attack into Russia to take the three major cities and their relevant assets: Leningrad in north (port), Moscow in east (tank facilities and govt), and Stalingrad in south (heavy industry and gateway to Baku oil fields). However, some predicted that Hitler (ever the amateur historian) wanted to avoid making the same mistake Napoleon did in invading Moscow first, which is set much farther east than Leningrad and would take much longer to reach. You have to remember that the Nazis crossed the Bug River in late June, meaning they had less than 4 months to march 1,300 km through the Pripet Marshes and fighting battles of encirclement, not to mention avoiding overextending supply lines.

The tactic Hitler favored was to launch the three pronged attack, but tier it chronologically so that he could take Leningrad first, then use those victorious forces to bolster the invasions of the Donetsk basin. Moscow's capture was to be mostly symbolic, a sort of morale crusher to cap it all off, and he didn't even think the city was all that important strategically. Of course, this stubbornness bit him in the end, when his generals tried to explain that a decisive victory in Moscow might actually help in Leningrad and Stalingrad, where assaults had stalled.

Hitler, as luck would have it, wasn't big on listening to his generals after the Fall of Paris.

If you're interested in more details, skim through the first few chapters of Alan Clark's Barbarossa. My Russian history professor referred to it as an "oldie, but goodie."