Dig out as much of the wood chips as possible. You will be left with a pit and even then there will be wood chips mixed with dirt. Fill the pit with topsoil. Mound over the area with dirt because there will be sinking over time as the remaining chips and roots decay. Then sod or plant as appropriate for your area and the type of grass (I'm unfamiliar with your seasons). You can sod most anytime. You will need to water unless you have rain. Grass in the areas where you cut down the trres will likely not grow as well as the rest of the lawn and will need more nitrogen. The wood chips down in the dirt will be depleting nitrogen as they decay. I had a big tree removed late 2012 and I spent several weeks in February moving wood chips. I used them as mulch. It was a very dirty, laborious job. Shovels don't work well. I picked at my mountain of chips with a hand trowel. I probably should have had the stump grinder remove them with heavy equipment. You definitely need to get them out before trying to grow anything there.

Thanks, beckybeck. Will do!

Not to be disagreeable, but I believe beckybeck's approach is the same one that gave your the eternal depression you were trying to avoid. Burying the roots will give you a never ending problem. When I say never ending, I buried a stump 20 years ago underneath compost. I unburied it after 15 years, and it was as solid as the day it was cut down. I took a different approach and turned on a misting nozzle over top of the stump. Within 3 or 4 weeks of continual misting I had mushrooms forming on the wood to begin the rotting process. 18 months later the stump is completely gone leaving nothing but a very soft spot. The spot is behind my garage so I haven't really done anything with it, but at least I am confident the stump is no longer an issue. Throughout the 18 months of decay I used the mister only when I thought it was getting too dry. In your area that might never happen. But all I had to do was get the rotting process kick started with the continual moisture and then I let Nature take Her course. You must have an open air access or the wood will never rot away.

Burying it with soil is the common mistake. My approach will speed up the decomposition process so that you can at least get the grass back in there and level in 2 years rather than chasing the devastatingly slow decomposition when you bury it.

GarlicCity has had the stumps ground. He has piles of wood chips, not stumps. I recommended removing the wood chips as best as possible and filling the resulting pit with dirt. Some roots are ground with the stump but there are still lateral roots in the ground and they just have to decay over the years. I can't imagine digging up all the lateral roots for a sizable tree. An alternative approach would be to leave the piles of chips and mist them, as Dchall suggests for stumps, but it will still take a long time for chips to decay. Even when they are decayed, I think you'd still want to dig out the decayed chips and replace them with dirt.

I thought it would take a long time to decay, but I was willing to wait it out. It took a total of 18 months until the hard stump had become soft as a wet sponge. When I stepped on it my foot sunk in (kinda gross). It has been a couple years since then. I should look again to see what the condition of the former stump is. Chips would decompose faster once they process starts. My suggestion was mostly to get the decay process started. Once it is started, it cannot be stopped except by cutting off the air supply with soil.