Moved into a new house, blank Slate in the backyard trying to design right now my vegetables, but I need to figure out where to put the chickens only a small 4 to 6 birds
Where are you located? Climate plays a HUGE role in caring for chickens. What works for me in Michigan probably won't for someone in Florida or Alaska.
You can add your location to your profile, and then it's there, and people don't need to ask. Just the state is fine, or the country, if you're not in the US.
Here are the usually stated minimums for chickens:
4 sf/bird in the coop
10 sf/bird in the run (15 is much better!)
1 linear foot of roosting space/bird
1 sf ventilation/bird in the coop, open 24/7/365
Note: "open" ventilation means covered with hardware cloth to keep out predators.
Strongly advised: Build the coop/run as big as possible. The chickens will be much happier. And then there's chicken math...
I had chickens in Northwest Arkansas, similar climate.
My first consideration is drainage. Your coop and run need to be where water drains away from it, not to it. If it stays dry life is a lot easier. If it stays wet life can get very bad.
You will see some pretty hot weather in summers. Shade for the coop and for the run is good.
Your winters aren't that bad. As long as they stay dry and have a way to get out of the wind you should be OK.
Your garden needs full sun.
I do not want the coop really close to the house because of potential noise and potential smell. It can draw flies or other pests. Your coop/run do not have to stink but if the weather sets in wet they can.
I do not like wading through water to get to the coop when it sets in wet. Consider the path you'll take to get there.
Where are you storing the chicken feed? Consider carrying it there when you buy it and consider carrying it to the feeders. You want it convenient to you. Same considerations for where you are getting your water.
I like the garden fairly close to the coop and run so I can toss garden excess and scraps in the run for them. If you build a compose pile for the poop relatively close to the garden (for scraps) and coop (for poop) is convenient.
These are the things I'd consider. Most important is drainage.
All I can add is figure out what direction your strongest annual winds come from, and your coldest annual winds. You want walls of your coop on those two sides. The narrower wall (if its a rectangle) into the strongest winds. If the coldest and strongest come from the same direction, next consider the wind direction on your wettest month.
That gives you your orientation.
@Ridgerunner has great advice above for location and the improtance of draining away from the coop. @Sally PB on sizing.