Singapore. It's essentially at the crossroads of most international terrestrial trade and transport routes and already has highly sophisticated logistics infrastructure.
Singapore is in an impossibly bad position for a space launch site, as e of pi said, whatever its other virtues. There's no range worth speaking of, and the very business that makes it logistically attractive means its impossibly risky to actually use; even the ocean has enough ships that there's a nontrivial chance of dropping your boosters/first stages on someone's head.
In any case, the actual logistics loads of actual spaceports are not too high
per se, since all but the very very busiest don't actually
do much, the main problem is keeping reasonably close to manufacturing sites and being on the coast; this is why despite early proposals by von Braun, Christmas Island (the Pacific one) was never actually used as an American launch site, and Guam or Hawaii were never seriously considered. You can also look at SpaceX's use, or rather non-use, of Kwajalein once they stopped building the Falcon 1. It proved to be so distant from the manufacturing site that despite the performance advantages it was unattractive for actual use.
Similarly, since White Sands first of all had no access to the sea and hence barge shipping for oversized first stages like the S-IC, and second of all had no coastline anywhere nearby, meaning larger rockets would pose an unacceptable risk to nearby populations (and yes, there
are people who live near enough to White Sands for that to be a risk, for example El Paso), it stopped being really used after the first few years of American space research, and most activity shifted to Canaveral or Vandenberg. There was some consideration of using White Sands as a launch site for Shuttle, especially early on when Shuttle wasn't supposed to be dropping boosters, since it could be an all-purpose all-azimuth site, but the lack of infrastructure compared to Canaveral and Vandenberg sunk that one (I've also heard the sands of White Sands caused problems on STS-3, which did a landing there as an alternate to Edwards, but I'm not sure of their exact nature).
Baikonur was a bit of an exception to that, but the Soviets had few good choices, and overall they did about as well as they could. Note that Pletsek is much more conventional in location, except for being near water (they were shipping everything by rail anyways, after all).
So what you're really looking for is a site which is close enough to major shipping routes that it's not problematic to have traffic come by, but not so close that there's a risk of falling parts landing on important shipping, while having sea access and a large clear range to the east and, preferably, south or north (for polar launches). Being near the equator is also handy. East Africa is probably your best bet for the total package, although as noted earlier political and infrastructural issues would be a problem. The tip of Somalia is probably one of the best overall launch sites in the world, rivaled mainly by Brazil's Rio Grande do Norte.
Of course, if you're operating under non-historical conditions, like having space elevators or fully reusable launch vehicles and a great deal of space-Earth traffic, then the ideal would be somewhat different.