Oh, this is easy. In the fall, aerate the yard, REALLY aerate the relatively bare spots and seed the crap out of it....maybe even throw down some top soil on top if the bar spots. Until then, manage weeds with treatment and mow regularly. Construction destroyed our yard last year and the sod they laid (because of timing) ended up dying off because of brown patch, so last fall I had a completely dirt front yard. We aerated the crap out of the yard and dumped an entire 50 lbs bag of seed on the front (about .3 acres).
This spring, the yard looked similar to what you have now. I then focused on the bare areas, aerated the crap out of the areas, dumped seed and top soil on top if it and it's coming in pretty nicely. By the fall, it should be all set....just in time for the new owner to take over