I'm not a bow hunter, but next year NY will allow cross bows.
I can see myself getting into cross bows.

Typically, how far does a deer run once hit with an arrow?

I know rifle hunting, they can drop, or they can go 100 yards...
But I have an oppurtunity to bow hunt on a very very small parcel.
and I can't go tracking across other property.

Read this Post it will tell you everything to expect from an arrow shot deer

i have tracked a deer that one of our hunters shot in the neck with a bow and tracked over a mile in half before we found in piled up.

If you put an arrow through the lungs like you are suppose to then a deer typically will make it 40 - 100 yards. Usually closer to 40.

what do you consider small lot? 5 acre? 10 acre? 100 acre? etc..
with gun, yes deer can run but generall force of impact have them laying down fairly close,
with a bow which relies on bleeding the deer,
good shot can keep the deer close, but have greater chance of deer running longer distance,
also with a bow shot deer its more important to wait before tracking, 1-4 hrs depending on shot, as can easily push a deer further before it bleeds out,

If you make a good shot you can watch them fall most of the time. If you make a bad shot you'll have a bad day or two.

After reading everything, I may not do it. My buddy only owns 2 acres, and there is a house every 2-3 acre's around the area.

It would have to be a perfect shot with a cross bow, which I know is not happening as a novice bow hunter.

It will only be legal in regular gun season next year - not early bow.

It doesn't matter whether it's a conventional bow or a crossbow. There is a broadhead on the front of an arrow which causes interanl hemmoraging if placed in the right area (chest/lungs). There is a broadhead on the front of a crossbow bolt, typically the same kind and which does the same thing as that on an arrow. The results are usually very similar.

The only variable is that it is usually easier to aim and place a bolt into the desired spot, but not always. Just as in gun hunting a deer might not be angled just the way it appears to be, meaning a possible marginal shot placement.

Personally, I'd look for a larger parcel of land to hunt given your experience and your own thoughts on the subject. You also may have to consider state laws on safety zones, meaning how close you're allowed to hunt to occupied buildings.

You might hit a spot like the spinal column that puts them down on the spot, alive for a bit but unable to use their back legs . . . that's NOT the spot to aim for. If you hit the heart/lung region that nearly every bowhunter aims for, you'll most often have them hit the leaves in less than 100 yards - usually significantly less.
Practice a lot and try to simulate conditions & positions you could encounter while hunting.