Dear Joe, 

Both wild strawberry and blue violet are good choices.  You may also consider Pennsylvania sedge / Carex pensylvanica.  Pennsylvania sedge can handle some foot traffic (not daily), and high mowing, but is not competitive against weeds, so it may not be a good choice.  I'm not aware of any natives that are competitive against dandelions - maybe wild strawberry.  

Carex pensylvanica Pennsylvania sedge

Pennsylvania sedge has a wide distribution throughout the eastern and central U.S., with one form, C. pensylvanica var. pacificum, reaching all the way to Puget Sound in Washington state. With such a wide distribution in nature, this sedge and its hybrids hold much promise for natural lawns of the future. Typically found on sandy soils in dappled shade or as a constituent of low prairies, Pennsylvania sedge can tolerate less than ideal conditions in the garden. Its noninvasive, creeping foliage forms dense mats of medium green, fine-textured foliage growing 6 to 8 inches unmowed. As a mowed lawn, this sedge looks best cut two to three times per year at 3 to 4 inches high. Plant Pennsylvania sedge from plugs 6 to 12 inches on center in fall or spring.