By now, it's pretty clear global warming is occurring. While there is still nearly a one in a million chance the wingnuts are right that it's not caused by humans, that doesn't mean we don't need to do something about it.
Grass, a plant that many Americans seem to worship, is unfortunately not a good plant to be wasting space for. Between the grass storing less carbon than other plants, raking leaves and getting rid of them to help the grass grow, chemically killing weeds, cutting the grass, and watering the grass, it causes a lot of problems.
Grass stores very little carbon compared to, well, any other plant. Even native prairie grasses such as eastern gamma grass store more than five times as much carbon as the grass people grow in their yards. Shrubs, especially those left to grow without a lot of trimming, store more carbon, and trees, especially older trees and long-lived trees with large trunks, store a lot more.
Planting shrubs also increases shelter and food for birds. Here in Rockford, IL, one of the most common shrubs is yew bushes. They can be trimmed to any shape, require no extra watering, are evergreen and provide shelter to birds in winter, and produce a few berries for birds to eat. Of course, there are an awful lot of deciduous shrubs that produce berries, and there are holly bushes as well.
Planting trees helps even more. There aren't enough trees in the cities in general, and they can store some carbon. Every tree helps. Oaks, poplars, sycamores, sweetgums, and other long-lived trees that form large trunks store the most carbon - but larger trees store a lot more, so the sooner more trees get planted, the better.
Vegetable gardens may not neccesarily store a lot of carbon, but by growing your own food, you're also reducing emissions from transporting food and creating packaging for that food to be shipped in, as well as probably using less fertilizers and pesticides growing it. Of course, if you're going to grow vegetables, the best way is to chose plants suited for your area (for soil pH, temperature, and water).
Compost heaps can be quite usefull. For best results, use a raised heap in full sun with wire around it, and tie tomatoes or other plants that require staking to the outside of it - and plant cucumbers, zuchini, or melons near the top of it. It will heat up more than the surrounding area, so is a good place to grow heat-loving crops (like watermelons).
As for flower gardens, the traditional weed-free flower garden with mulch between plants is pretty bad, and substituting stone for mulch is the absolute worst. Yeah, it looks nice, but it's truly wasted space. Plant flowers that don't require massive amounts of watering in your area.
There's also a few plants that are edible that can be planted for flower gardens. Some mallows (M sylvestris in particular) have leaves that are edible, and grow easily in flower gardens. Flowering kale is edible, and the tubers of daylillies are edible. Elderberries can be planted as shrubs, and the berries can be made into jam.
If nothing else, at least mow your yard less often. That at least allows it to store a little more carbon, and reduces the amount of emissions made by your lawnmower (lawnmower engines are often very inneficient). But if we're going to slow global warming, we're going to need to do a lot of things. We absolutely need to stop emissions of carbon and other greenhouse gasses... but we'll probably need to redesign the way we live also.