I'm not sure what you mean by pre-loaded, but is it that much cheaper to go used? I just checked sofmap.com and they're offering used PSP for around 17500 yen (plus 1% on point card)...while you can pick up a new one at yodobashi for 20800 yen but with 10% on their point card, which would get you a greatest hits level game for free (Wipeout pure is a good place to start your PSP experience off with)...so there isn't all that much in the way of savings going used and a new one would have a full warranty as well and you would likely have more color options as well. Actually, due to firmware upgrades that were less homebrew friendly, there have been times in the past when used PSPs, with their more homebrew friendly firmware versions actually sold for more than new units....but I don't know if that's still the case nowadays.
But if you are set on going used and going to be in Shinjuku, check out sofmap http://www.sofmap.com/tenpo/shop/shinjuku_area.htm (#2 Soft collection) or Trader on Kokusai dori one block north of the sofmap #2 and about 30 feet to the west....It looks like they only have software from the street but they have hardware in the back of the store.
That said, while there have been rumors of a PSP redesign for years now, I'm starting to think it is more likely than not at this stage (plus with a bazillion DS-es out there, Sony needs to sex up the media functionality of the PSP, since its pretty clear that gaming alone isn't going to save the system or at least until they add a second analog control pad.)...There might be more about this in about a month or so when E3 rolls around.
The Enrichment Center reminds you that the weighted companion cube will never threaten to stab you and, in fact, cannot speak.