Ant diversity isn't very high in my area, unfortunately.
Species likely to be found in your average Dakotan yard-
LOTS of Lasius (normal to parasitic 20:1, about)
LOTS of Solenopsis molesta (many colonies have multiple queens, and display impressive color variation and macrogyne/microgynes)
several competing colonies of various Formica species, most or all from the fusca group
maybe a Camponotus colony or two
a few Ponera colonies
in some areas a couple Tetramorium immigrans and tsushimae colonies
in my yard I found a couple Dorymyrmex cf. insanus colonies, not sure how common they are, extremely elusive
maybe a Brachymyrmex colony
maybe a colony or two of rarer species