Question
Does any website, lets us test SharePoint 2013 basic features?
Solution
CloudShare has the option of spinning up SharePoint 2013 environments if you want to test on-premises
Office 365 has the Sign up for an Office 365 Developer Site if you want to test the upcomming Office 365
OTHER TIPS
You can try the new SharePoint 2013 through Office 365 preview:
http://www.microsoft.com/office/preview/en/try-more-products
Training Videos can help you getting the basic training in SP 2013. for testing it online better go with Cloudshare, but it is always good to test it locally as you will not able to test the complete features in cloudshare, like in local.
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