Depending on how big those knotweeds are, there's likely not going to be a whole lot of anything coming up from underneath them, once you cut it. I'd suggest being careful, because it's taken almost a full year of constant observation to make 100% sure I got completely rid of the first patch of knotweed I pulled out. After starting the patch last spring, I only just guaranteed within the past two months that it's completely cleared out.
Once it's gone though, things that might grow well there (and quickly) include:
Eastern Redbud, Pawpaw, Carolina Buckthorn, Black Elderberry, Chokecherry
Highbush Blueberry, Blackhaw Viburnum, Eastern Sweetshrub, Goose Plum, Beautyberry (if you're pretty much right on the southern border of the state, but you might be ale to get away with it?), Clove Currant, Illinois Rose or Swamp Rose, Black Raspberry/ wild Blackberry/ dewberry
Partridgeberry, Jewelweed, any number of other Native wildflowers or grasses, Eastern Yampah