Besides the usual; Dealer, Here, Places like the moped juck yard (I'm not sure if they carry honda) you might also look at Ebay. Be very careful on Ebay though, you don't get the opportunity to turn the used pieces around and inspect them but you can sometimes get a good deal off of there. Do a search using Honda Moped and Honda express and see what you can find. It also helps to do the same with the option to look at auctions that have ended to see what other parts went for. Depending on the demand, you can sometimes get some very good deals. If you get too ancsious about the item you are bidding on though, you can end up bidding too high and paying more for what ever it is that you are buying.
I've noticed several Honda express items that went through the whole auction with no bids. There were several simmilar items on sale at the same time. I've bought a lot of parts from Ebay for a Suzuki Fa50 that I fixed up. A lot of the prices were quite cheap and on a few items, I paid too much. a few examples of good buys that I got from there:
tire, regular 18 to 26 from differant web stores, on Ebay I paid $5.00 for a new one
Air filter box (the only place I could find one was the dealer) Ebay, 10.00
Whole motor with trans in good working condition Dealer price (forget it, buy a new one cheaper) Ebay 37.00 minus the carb (they have had better ones go for even cheaper but the shipping was way low on the one I bid on)
Speedo with ignition switch Ebay: $12.00
Ignition coil, Try $3.00 on Ebay for one in good shape!!
Rear fender Ebay (never got shipped, I got screwed!!) But I did get my money back after a bit of a hassle. New handle bars I got a new looking set on Ebay for something like 4 bucks.
If you can wait for the right deal, you can make out like a champ. If you need as many parts as I did, You would actually be better off buying a doner bike (maybe)
Post a request for what you need in the buy sell portion of this forum.
Look on Ebay
Check out the normal locations like themopedjuckyard.com mopedwarehouse.com stevesmopeds and the link areas for honda mopeds
BTW, it always helps to post what it is that you need when looking for parts!!