How can I use images from my live Craft Site when developing locally
You could set up your assets through Amazon S3 or another remote service then that wouldn't be a problem.

Alternatively you will need to download all the assets locally if you have relative paths /uploads/images/banners/banner1.jpg.

Though maybe another option is to set the path to include the domain then you can probably get the files from the server (so in your markup you would see the image would be linking to http://www.yousite.com/uploads/images/banners/banner1.jpg