Agree with Floral_uk, it looks like one of the black nightshades, probably S. douglasii given your location. There are several very similar species, and they grow wild pretty much everywhere. I take great pains to ensure that they never go to seed in my gardens, and they still crop up from dormant seed or from bird droppings. When I lived in San Diego, the local Hmong community cultivated one of the black nightshades extensively. There is a pretty god write up of the various species & their properties in the link below. Personally, I would just treat it like the weed that it is & dispose of it. Really nice jade plant bush behind it, by the way. Here is a link that might be useful: Black nightshade

a few plants come to mind when you say baby's tears; Soleirolia Soleirolii, Sedum album var chloroticum, and Pilea depressa. Baby toes is another plant alltogether. Good luck :)

peruse a few of the posts in the name that plant forum.. and see the type of pix you need for good IDs ... these pix are near useless for ID purposes.. though chris gives it a yeomans try ... there is a west coast conifer.. that looks like the juniper suggested.. but the name is escaping this MI boy .... if you take a walk around the area.. and snap your own GOOD pix .... and post them to the name that plant forum.. including location.. big city name.. those peeps can ID anything .. with the benefit you know they will grow where you are.. include local parks .. arborteums.. and nurseries ...which of course.. should have labeled plants ... ken psw: btw... that second pic looks heavily photoshopped ... something about the balls under the trees in dead center ... which makes me question the whole thing ...

You can get pink spiky flowers from Veronica, Salvia, Agastache and Obedient plant. You'd have to find cultivars with the right height and color. The fuzzy purplish spikes in the front part of the border look like perovskia to me, but it could be lavender. You'd need a short cultivar of perovskia. Between the pink, there are other plants, probably to bloom at a different time. My hydrangea bloom later in the summer, so you'd want some spring blooms. Between the lady's mantle (alchemillea mollis) and lamb's ear, there's another plant. Hard to identify, but I might suggest a moss phlox. It will bloom in the spring and you can get them in pretty much every shade from purple to pink to white. They should be native to you. I hate lady's mantle. It spreads like crazy and is hard to get rid of. It looks lovely only when a few dew or raindrops are on the leaves. It gets dull in the summer heat and I'm in Maine, on the coast, so almost certainly get less summer heat. You might put in a lime-colored heuchera in its place. You'll get the lime (the color of the lady's mantle flowers) year-round, heucheras are native (lime is not a native color, though). And you won't get the stuff in your lawn. The heuchera won't like too much sun, though. So, bottom line is check sizes to ensure you get cultivars that will be the right height for your design. Check bloom times so your garden has something blooming in all seasons, and check for sun/shade.