Depending on where you live, you could start with introducing clover into your yard. It grows well in most of the US, tends to be more drought tolerant than many grasses, is easier on the soil (requires less soil treatment), and flowers nicely part of the season, which is great for bees and other pollinators. It will co-exist with grasses, so you don't need to do anything beyond tossing seed in the early spring and letting it germinate, just as you would do with grass seed.
Weekly maintenance is similar - just mow it (though let it grow long when it's flowering - cut off the flowers and you lose the pollinators).
I'm in the UK. My lawn is about 1/3 clover already, as it happens, just by natural process of it being stuff that grows better in the conditions on that part of the lawn. I don't consider that to be not-a-lawn, it's fairly normal I think, and the management is no different to the grass. (My 'lawn' overall is about 1/3 grass, 1/3 mostly-clover, 1/3 mostly-moss: the grass grows well on the sunny side, the moss beats out everything else on the side that's almost perpetually in shade by the south-side fence, and the clover wins in the middle-zone between them.)
I only half-joke about cultivating crab grass; it's green, grows flat so never needs mowing and is drought-resistent. I never walk on the lawn in our front yard and could really care less about what the neighbours think. Resists inconsiderate dog-walkers as well...
Not really, but I hate the stuff. I finally managed to get most of it plucked out of my front yard. Hopefully the additional clover will displace it fully next season.
Weekly maintenance is similar - just mow it (though let it grow long when it's flowering - cut off the flowers and you lose the pollinators).