Native plants in the landscape is a topic that is gaining much momentum and popularity. The benefits for wildlife are well documented, and you can enjoy an urban or suburban oasis in your own back yard.
You do not have to rip out your entire landscape, but rather incorporate native plants among your existing plantings. The Asian species of rhododendron in my side yard was planted by the previous owner, but now Herb Robert, Geranium robertianum (considered a native by ODNR) scrambles about the hosta growing beneath it. Front and center, a native blueberry, Vaccinium corymbosum dangles white balloon-like bells destined to become familiar blue fruits. You can have your landscape and eat it too. Or better yet, leave it for the wildlife.
Scatter plantings of columbine, Aquilegia canadensis or jewelweed, Impatiens capensis within hosta beds to attract humming birds. You will love the results! Non-native plants can co-exist, as long as they are not the incessantly invasive types.
In my yard, invasive species i.e.- honeysuckle, garlic mustard, multi-flora rose and purple loosestrife are given no quarter. They are treated as harsh as a terrorist in an international airport. Zero tolerance. You get the picture.
Many fine publications and books have been written on native plants in the landscape and it is one of my favorite topics when giving programs. Another excellent source for information is the Wild Ones, with multiple chapters in Ohio, including Toledo, Columbus, and Cincinnati; you should be able to find one near you.