First, make certain you are logging in to the same account. If it's the same account, all of your games should have shown up in the game library in Origin when you installed it. If you're absolutely certain that it's the same account, and you can't find your city, it depends on whether you're playing online or offline.
If you're working online, your cities are saved on the server and should be there. Make sure you selected the same server. You can try copying the game files from your old computer to your new one. Default location for the game files is C:\Program Files (x86)\Origin Games\SimCity, just copy the old computer files onto a thumb drive and transfer them to the same place on your new computer, overwriting any files that are the same. That should make it open at the same place so you can find your city.
If you're working offline, your cities are saved locally on the old computer's hard drive. Mine are in C:\Users\<User Name>\Documents\SimCity\ (I *think* that's the default location, but I could have changed it. It will have folders called Games, Movies, Pictures) Copy the SimCity folder onto a thumb drive and transfer it to your new PC in the same location. Overwrite any files that are the same.
Be aware if you're working offline that the game only updates your local copy, there's not a copy on the server. So playing on the new computer will not update the old computer's version.
Hope that helps!