Pretty much every formal attempt at creating a list of "most important cities" places New York at the number 1 spot, with its strength as an economic and cultural centre going far beyond it not being a seat of government.
It is this importance which makes it, for the purposes of the challenge wanted by the OP, critical to decide if it would be ranked in the top 5 at 1900 as well. There are good arguments as to why it might be so - it already had a larger population than all European capitals (save London), it was already a major financial centre, and the United States as a whole had an economy that already competed with that of the British and German Empires for that of largest in the world. If we do place it there in 1900, it makes our timeline much easier, as the rising might of the US (and New York) are at that point impossible to avoid without resorting to nuclear war or a cataclysmic series of natural disasters.
London and Paris also tend to make most lists of "top important cities", due to their still extremely high economic, cultural and human capital. Since they manage this OTL, then it's probably safe to say that any scenario that avoids the decline in Europe's influence (which would be needed to keep the relative power of its cities up there) would easily keep Paris and London in the top five.
The biggest challenge would then appear to be Tokyo, which has "led the pack" in Asia's economic rise, and as the world's most populous and economically rich city, is pretty much assured a place in the top five in 2011. It would not have been so in 1900. Japan, whist developing, was still a lesser power compared to most European ones, and Greater Tokyo was financially junior, even within Asia, to cities like Hong Kong and Shanghai. If Tokyo is taken without Yokohama, then it would not even have been a competitor in 1900. To stop its development you likely have to manage to halt the economic development of both Japan and Asia, which is hard to do - the former because it had already started (and a destructive war was not enough to do so OTL), and the latter due to the sheer weight of demographics. But a combination of some series of "humiliating" wars, internal isolationism and a nudge to higher development of European powers should help keep Tokyo out of the top five, though it might still be quite important.
If we include St Petersburg in 1900, then having it still take the place in 2011 is fairly easy. Just keep it as the capital and avoid the myriad of ills that plagued Russia (and the city in particular) in the last century - The Red Terror, The Civil War, WW1 and 2, Stalin's Purges, the collapse of the USSR - OTL was such a Russoscrew that avoiding it means that, by virtue of its existing position as Russia's political and financial centre, the sheer weight of the nation's demographics, institutions and resources would keep it in that position until 2011. If we do not include it as such in 1900, then taking away its status permanently wouldn't be too hard either - Russia was already in the midst of revolutionary fever, and damaging it without the rest of Europe suffering too much isn't that difficult.
Berlin also makes a good candidate as a "top" city in 1900, though to a lesser extent. Whilst it was the seat of the German Empire (by many measures, Europe's strongest nation at the time), unlike Paris/London/St. Peterburg, it was not its Financial one - a title reserved for Frankfurt. Further, its role as the capital was still a fairly young one, and it had not accumulated much of the cultural and intellectual strengths that characterized other European Capitals. On other hand, economically it was growing rapidly, and arguably be Europe's industrial centre within decades. If we include it in 1900, then keeping its status up to 2011 would require us to avoid Germany's catastrophic wars with the other European powers - which is hard to do whilst still keeping Paris in the top 5. Best way to do it would be to alter the balance of power in Europe to the point where any war is one-sided enough to end quickly and painlessly. That would probably require aligning the British Empire to Germany (which the Germans certainly wanted to do). The best timeline for such would likely combine keeping the "Great Game" Anglo-Russian rivalry going and preventing the former from being too scared of the Germans (which requires less German expansionism). This has the bonus of Germany of greatly expanding German influence into Eastern Europe, thus further securing Berlin's power.
Vienna and Constantinople/Istanbul were both important capitals of Great Powers in 1900, with immense cultural heritage, significant economic power and great intelligentsia. Both Empires however, we also faced with large levels of ethnic strife and external pressures, which OTL doomed them both.
Istanbul, while much smaller, is probably the easiest of the two to keep strong in 2011 if the city's rapid rise in economic power and population in the last few decades is anything to go by. Keep the Ottoman Empire alive, and the city's pre-existing geographic location and status as quite possibly the most international in Europe, coupled with the earlier start of a "boom" like OTL's, would be able to get it a spot in the top five. If we go along with the aforementioned "Britain aligns with Germany against Russia" timeline, such a survival becomes much easier (With the Ottomans joining in on the war), and even if the Empire's weak financial and political situation would likely mean it being eclipsed temporarily, survival could buy it enough recovery time to make it back into the top 5 by 2011, especially given all the Oil it gets to keep.
Vienna was, by many measures, likely more influential than Istanbul however, being the seat of a stronger empire and having started industrialization earlier. At the same time, keeping the Dual-Monarchy united and strong is probably harder than it would be to keep the Ottomans together, given the much more widespread ethnic composition and internal problems. Making Vienna as influential in 2011 as it was in 1900 would require a fairly inventive timeline, as "Europe doesn't get screwed" alone won't be enough.
If Europe remains strong, keeping other areas of the world from eclipsing them will be somewhat easier. China, the biggest challenger, was in the midst of the Boxer Rebellion in 1900, being suppressed by the very same nations. China will still remain a formidable challenge however. Some of its Cities were easily in the top 20 in 1900, and they have managed to increase in influence despite over half a century of misfortunes such as civil wars, invasion and insane government initiatives. Since European interference will likely replace, rather than augment, many of these negative developmental influences, most timelines that do not feature some kind of nuclear exchange will see Chinese cities at the very least challenging some European ones for the number five spot.