Native grasses for woodlands include many of the sedges or Carex. C.Pensylvanica is an easy woodlander for somewhat dry to moist part shade. It is under one foot. I also like C. plantaginea, the wide-leaf sedge. There are many others, but not all are short. For your open meadow, you may have difficulty finding many grasses and wildflowers that are under 12 inches. Most meadows contain a mixture of tall and short plants, both flowers and grasses. Buffalo grass is very short. You could investigate that.

Short to mid-length prairie grasses used commonly down here include :
Buffalo grass - 4-8"
Blue Grama grass - 5-12"
Side Oats Grama - 8-18"
These are all bunch grasses. Look for a company that sells native grasses in your area, or at least your zone.
There may be other grasses native to your area that we don't have down here.

The height you want is a hard one .... usually 'short' means about 2-3 feet. The suggestions already given are good ones but here are a couple more not listed.

Juncus tenuis - path rush 1' tall, dry soil, sun to part
Muhlenbergia cuspidata - prairie satin grass 1' tall, dry soil, sun
Carex rosea - curly styled wood sedge 1' tall, dry-mesic, shade to part shade
You may want to consider spring ephemerals for flowers...they die back once they've bloomed. Otherwise there are violets that are under a foot tall.

I hope you can post some photos.