You can search for hotels by entire state (go through Advanced Search), but in that case it makes you click through two levels before you see the price (whether in points or money), so I don't think that helps you that much.
Have you considered the most old-fashioned way? If you can still find a printed directory (they used to be in all rooms a couple years ago, but I no longer see them in my rooms, but perhaps they're still available on request), I think it may have mentioned the point requirements in there? (I don't have one handy to check, though.)
Have you tried calling them and saying "your promo states that the 8000 points I earn for 2 stays is valid for one night at over 1000 hotels, how do I find those 1000 hotels" and let them kick it up and kick it up until you get to someone who can admit that this claim is a bit bogus if there's no way to find those hotels? (If you wanted any other level, that approach wouldn't work, but they do advertise specifically that 8000 is "good enough" for over 1000 hotels!)
Doing the math, "over 1000" is roughly around a quarter of their properties, right? Given that few properties near big cities (except maybe EconoLodges

) are 8000, that implies that a substantial portion of small town properties are likely to be 8000. If you make that assumption, the "by state" search might actually be slightly useful (you could look over the list of locations in each state that sound interesting and "sound cheap", and then click through to see if my theory is right). FWIW, I can't click through to check how many points a hotel takes because I don't have enough points for
any hotel right now (having just done a transfer to miles the other day, and no stays posted since).