First things first, from what I've heard, this was unlikely, because Edo was at the time by a gigantic margin the biggest and most important city in Japan. Kyoto, by contrast, has historical weight, but little else tbh.
If, now, Kyoto was chosen because of the widespread paranoia about foreigners, then I think that it would be indicative of a wider and probably more influential current of 'anti-foreigner sentiment' which could both impede reforms and lead to the earlier development of a 'going it alone' path. So, for example, being too overly enamored of foreign things becomes something more of an insult in this case (IOTL, AFAICS, Japan, particularly the leaders, had an almost unseemly rush to adopt everything foreign automatically, replacing whatever had existed before in almost every sphere of life).
On Japan's development, I think this could potentially lead to greater divisions between East and West Japan. Centralization at Tokyo was really a process that began hundreds of years ago under the Shogunate, and while it declined after the Restoration briefly, the re-establishment of Tokyo as the capital reversed this process. ITTL, Kyoto would receive at least some of the development; ie, the university established at Kyoto would be more likely to become Japan's premier university than Tokyo Imperial University; but more importantly, the infrastructure of modern central government, all the apparatus that was built up at Tokyo, would be re-directed to Kyoto. It won't be a complete re-direct of course. Edo was already a much greater city than Kyoto at the time, and centralization hardly reached French levels, but there are a number of factors that simply aren't transferable to Kyoto. Firstly, for example, Edo was a port city, Kyoto was not. Yokohama received a deal of development parallel to Tokyo of course, but Kyoto is a bit too far from any coast to serve as the gateway to the international world that Tokyo was; for this purpose, Osaka is probably necessary (which probably will lead to Osaka also becoming more important relative to Tokyo ITTL), creating a 'third center.' The difference here would be that the internationalization received by Tokyo and Yokohama would be entirely transferred to Osaka, so rather than Yokohama being basically a subordinate part of Tokyo, Osaka is a major city in its own right relative to Kyoto. Possibly, I think you could see the urban areas of Osaka and Kyoto merge the way Yokohama and Tokyo seem to have merged, despite being separate cities. But I think that the development of 'two centers' in Japan is basically quite likely; Western in Kyoto-Osaka, and eastern in Tokyo.
Probably more to be said of course, of course, but I have class soon.
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