Have a tree right in front of my crib. No, back yard ground is not rock hard...it's soft, sometimes mushy...patchy grass. It seems to absorb rain extremely well.
For the summer time, it doesn't seem like an attractive place to have guests on though. I have a nice sized deck though, so we hang out there. But I feel like 2/3rd of my yard is not that unusable for just chilling. I wish it looked more attractive, so to speak.
Lawns are actually much harder to maintain than many people think. Different grass types grow better in different conditions. I asked about trees because even within same types of grass, you can buy seeds that have been created to grow even in shady areas.
In new York youre probably best with bluegrass or tall fescue. Bluegrass has a deeper green color and once it is established it forms a very thick lawn that can take a lot of traffic. But flipside is that it takes longer to establish.
I asked about the ground because a lawn that has a lot of bumps/dips will end up being patchy bc of the way water collects (or runs off). Grass needs water but if the ground is always saturated with water it will die off from fungus etc.
Depending on the size of your lawn it might make more sense to just buy the turf and have it installed. As long as you make sure it never dries out it should establish itself relatively soon.
If you want to try it yourself I would buy seed from a reputable dealer (figure out the square footage of the yard to determine how much seed you need to buy) cut the grass as low as you can, get a metal rake and break apart the top inch or so of soil, especially wherever it is patchy. You can buy a handheld spreader that will dispense the recommended amount of seed. These are nice bc you can use them for fertilizer as well. Throw your seed down. Don't be cheap. I usually throw more than the recommended amount bc might lose a lot of seed to birds. Once you've thrown the seed down, make sure it is pressed down into the ground. Roll something heavy over it or if yard is small enough just walk all over. You will need to buy starter fertilizer and peat moss. Use the spreader to put starter fertilizer all over. This helps your seed to germinate and gives it nutrients to grow. Then throw a light sobering of peat moss over everything. This will help keep the seed moist. Roll over or walk over everything again. The seed has to be in contact with the ground in order to grow. Then most importantly is watering. Water early early in the morning and at least once more in afternoon. The lawn/seeds must remain moist in order to germinate. If it's starting to look dry use the garden hose and go over it. Never water at night.