Where would I buy gr seed or sod in NYC, which would be better?Is It too late?

I recently rented a ground floor apt with a private back yard in Manhattan,Of course it's surrounded by a wall, its shaded but adequete sun, I benefit from the trees next door , the outer edges have planters built and plants that already exist are growing nice. there is a walkway all around the yard and in the center there is a nice large big square of dirt(it would take a couple of pallets ofsod I would imagine, (the area was covered with wood chips last year by previous tenent.) I long to have this all covered with gr, I have a small apt and a yard 4 times its size.I have no idea how to go about this, timing , conditions , care etc.the space is way too beautiful not to create some type of habitat. preferably one where I can walk outside barefoot in the damp morning gr and "ground " myself , I can t afford to hire gardeners or landscapers, it's a DIY project. Any advice?