Well I am not exactly sure as to which exact format the tournament should take but what I do know is that the current way in which teams gather up in Japan for couple of matches isnt plausible. The same goes for basketball as well. Its just not possible that us locals can generate as much passion as the home supporters if the game was played in a 2 leg home-away format.
Fli makes a good point though. Anyway tournament that tries to incorporate as much teams as possible is bound to have problem with the toll travelling takes. But then again, when you see teams like Real, Man U, Bayern, Fiorentina and even Juve (I had a pleasure of seeing Alex doing some timed trickery stuff prepared by the newcasters ditto for Aimar

) come to Japan for promotional purposes then one must wonder if they really are concerned about travelling that much if they can get marketing exposure. After all, South American players seem to manage fine in Europe considering the fact that they go back and forth for WC matches. And most teams in Europe nowadays operate on a rotational basis anyway. The matter of fact is if European teams will have far more significant monetary benefits if one can actually arrange both Asian, European and South American teams to play in a competition that actually matters. This will be far more effective than meaningless pre-season matches they come in for and loose for whatever reasons. In case of Real, they sure became a laughing stock for a while. Getting thrased to relegation threatened Verdy was just an icing on the cake.
So my conclusion is that teams really dont matter about travelling that much as long as they believe they can get compensated for it. Moreover, I don't really see a significant drop off in quality of games played due to travelling. If anything else, I think Europeans could be surprised by the qualities in the other continents and over time one should actually see a convergence between leagues.
My best idea is that CL place should be somewhat expanded and allocated on the basis of past results achieved by each respective continent in world events. In a similar fashion to the oen currently operated by UEFA, which Erik kindly elucidiated, we can keep in check the balance between quality and diversity. Obviously this means that only one or two teams will get the chance to participate in Asia, Africa and North America, and a few more South American teams. We can even put pit these continents against each other to ensure quality of matches doesnt get degraded too much. The looser of this group get to participate in UEFA Cup. In doing so, I feel we should also limit the maximum number of teams in each nation, especially in Italia, Spain and England, since 4th place teams exactly world-beaters by any means and if teams in South America could get enough revenues to sustain its stars, I actually feel teams like Sao Paulo and Internacional, Boca Juniors will be better than Liverpool, Depor, and Fiorentina. Just look at Sevilla and Villareal - half of their players are from South America and apart from few exceptional ones - I bet there are many of equal perhaps even superior quality that hasnt come to Europe yet.
I am kind of favoring the extension of the current format and probably making some expansion of teams at the preliminary rounds to the other continents based on the international coefficients by each continent. I know FIFA won't allow UEFA to dictate the pace of global tournament moreover if UEFA has desire to do so, but this format is vastly superior to the one that is going to be played in a short time. And I think it is almost undebatable the general value of having world-wide club tournament.