Tradescantia blooms in the spring and then, if dead-headed, will rebloom later in the season. This one is called Osprey. I love the blue in the center. I also have them in all sorts of shades of blue, purple and rose. They are really dependable and will grow in sun or shade, though you will get better flowering in the sun. The common name for this one is Snotweed because of the runny sap in the stems. You get the idea.
Tovara virginiana has lovely variegated leaves and grows in the shade to part sun. There is another version called 'Painter's Palette' which has a rust colored chevron on the leaves.
The Tiarellas as a group don't seem to be bothered by animals. There are many different leaf patterns and shapes. These like shade and woodsy soil and bloom in late spring with spikes of light, airy, tiny flowers.
Tansy likes sun and will grow just about anywhere. This is the cut leaf form which I find much more decorative. The flowers are yellow and come in the fall.
Tannecetum partheneum, Feverfew, self-seeds readily in my garden. With all the rain we've had this year it is really going crazy. Usually it is about 18 inches tall and blooms all summer. This year we have plants 3 feet tall and I think every seed that fell last year has germinated. Even though I am weeding a lot of it out, it pulls out really easily and isn't something I would consider a problem. We have a plant here and there throughout the garden, and although I think it prefers sun, it grows well in the shade also.
Lots of thunder and lightning here last night and over an inch of rain. Great for the garden but it makes for a very muddy gardener after a morning of weeding.