I think it's Lilycove without a doubt. I just think that with everything being there (giant mart, contest hall, evil people base, the museum, the harbor) there's just so much going for it in terms of social, political, and economic advantages. It's obviously a major shopping center of the region, it has the harbor for imports, it has the history aspect with the museum. Yeah there's no gym to attract people, but there's the Master contest hall. I just feel like it's the ideal manifestation of a capital city.
If I had to choose a runner-up, probably Mossdeep. Idk why, I just feel like it'd make a good capital city. For all we know, that "space center" is actually a national defense base where weapons of mass destruction are being made for defense against the other regions. Or maybe it is a space station, but also a missile launch pad in case of warfare with other regions. If that's the case, I'd want Mossdeep to be the capital because it'd be the last to fall in warfare and at least then they'd have their weapons base until the end.
....I've taken this WAY too far just to make up a case as to why Mossdeep is awesome....