It's possible that you received a defective watch. I had an iPhone once with the same problem out of the box (I think it was my old iPhone 5). If I was in the same room with the router it would work but that was it. I was trying to determine if it was something with my router when I pulled up my iPad, my Mac, and this iPhone and scanned for wifi networks: both the iPad and Mac showed my neighbors networks but the iPhone only showed mine. I took it to the Apple Store and they said it tested fine but offered to exchange it on the spot and the replacement was fine.
Unfortunately you can't scan for wifi networks on your Apple Watch so it's harder to test this out. The wifi is super strong at the Apple stores so they may say it's fine like they did for me too. Since you just got this watch you should be able to return or exchange it anyways. Good luck.
