Are there any hosted online store solutions (a la Shopify.com) that are compatible with bitcoins? Are there any hosted online stores that can be set-up easily to take bitcoins?
AFAIK there are no publicly available out of the box solutions for setting up a store that uses Bitcoin. Although; there are many viable solutions using Bit-pay, their system integrates well with most platforms. If there is a platform you want to use their system for, their sales team can surely help you do that.

I have no affiliation to Bit-pay but spoke with one of their founders in length at the Bitcoin conference.

I would recommend looking into setting up a wordpress site (hosted, not wordpress.com), using ecwid shopping cart, and asking bit-pay to integrate the store into ecwid for you. 

This setup is a 99% one size fits all, and you would be pioneering the way for others to follow. Bit-Pay may have an alternative solution, but I have developed several online stores (10+) for clients - and use wordpress/ecwid for both of my personal stores (after trying many others).