First - you didn't specify if you use Bitcoin Core or any other program for maintaining your wallet, so the answer below presumes you used Bitcoin Core.

The short version: it stores all of its data in %AppData%\Bitcoin This folder usually translates to C:\users\\AppData\Bitcoin

Underneath that folder you will find there the 'wallet.dat' file. This is the file that has all of your addresses (including private keys). This is the file you'll need to copy.
You will find in that folder also a subfolder 'blocs' which is your local copy of the entire block chain.

On both Win7 and Win10 those files reside under the same folder - %AppData%\Bitcoin.

So - simple copy instructions:

1. Install Bitcoin on the new (win10) machine (and don't start it yet)
2. Stop Bitcoin on the old one
3. Copy %AppData%\Bitcoin\wallet.dat from old to the new one
4. You may also want to copy the entire %AppData%\Bitcoin\ folder with the rest of the files and block chain, or you can download it again (it's "only" 20+ gigabytes)
5. Once you're done with the copying you can start Bitcoin Core on the new computer.

That's all.

See https://en.bitcoin.it/wiki/Data_directory for more details.

You can indeed just send the coins to your new wallet on your new computer.

Downloading the entire blockchain is not needed, you can also use a light-weight client that does not require the full download

If you use electrum (http://electrum.org) you can store your bitcoins, backup them easily by writing your seed down on a securely stored paper and never have to worry about moving/backupping your coins again.

Electrum is a lightweight client that does not download the entire blockchain and is very fast