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Leaving aside Google, et al
Good sources of new sites are local directories (it's amazing how many startups there still are), smaller ISP's still quite often have 'our customers' lists. Other quite common sources are offline - Radio commercials, billboards, business cards, flyers, brochures (basically any normal business advertising activities).
If you are really looking for a subject, you can always use the Google alerts tool, yes it will show the the dross with the quality, but it will narrow it down, and is much easier that wading through the 30 odd pages Google will let you see.
Obviously each approach works best for different category types. The local papers classifieds work in small Regional categories, not so good if you are looking for sites for recipes on using hamsters in a curry. Radio/TV advertising may have urls about current events, concerts, celebrations, health , travel warnings, government information, even (dare I say it) shopping.
Will this help you target somewhere to get your sites noticed? Probably not. But it should make anyone reading aware of some of the ways outside the 'suggest a site' link editors can, and do, find new sites to list.
Is a hoarding one of the big plywood signs at construction sites?
Noone mentioned "submissions" and "other search engines than google" yet.
what about written into the dirt on the back window of my subaru?
Given that Tim Berners-Lee defined the U in URL to be universal (he was overruled by some Internet committee with no imagination): then, yes.
A URL identifies a resource. The resource can be anywhere (a website is just one possibility) and the URL can be anywhere too (in Google is a very limited possibility in some ways).
If you want an OPD editor to notice a URL, you got to put it somewhere where they will see it. For many categories, the last place they look is the suggested URL queue.
A hoarding is another term for a billboard. I saw the sign that said "New visitor attraction opening soon....http...". The site was up and running, so I added it.
Reviewing a site that was so totally bad it could not be listed, yet finding it linked to about 50 other sites that were good, 15 of those had never been submiited to ODP, and were then added.
Seeing posts in R--- Z---- where someone was asking about a site, but that person own sites had never been submitted.
Seeing an ad on TV.
Google alerts on very precise keyword combos.