Normally, there is no website which allows downloading things. Here is how we download: go to www.baidu.com and search "something 下载". If everything goes fine, you can get some torrent files or torrent links. Then you can use some software to download them. In fact, you can get any chinese cartoon on Youtube. So if you just need to watch them, I don't think you need to download them. If you want to watch them without Internet, you can download Youku app for you smart phone or ipad. With this app, you can download videoes. You can watch them without Internet as soon as the downloads are completed.

www.u17.com

Chinese cartoons are very very immature, in fact they are truly made for CHILDREN...You can watch Jp animation with Chinese subtitles，or movies instead maybe a good choice. As for webs, some popular websites we usually visit are forbidden outside China. Maybe you can find some on Youtube or sth...:)