Is it possible to display a 'shop by price' menu?

Something like
0-$100
101$-499$
500$+

and then display all the items in a category that fall within that price range?

Not automatically. However, you could create one category called "prices" which would be unpublished and containing these three price categories beneath. Then, for each product, you could add one of these three categories.
Then, you could create a new module of the type hikashop content module via the joomla module manager and set it display the categories beneath the prices category.

Upon clicking on one of the price category, the user would then see a listing of the products in that price category.

Thanks - is a bit of a fudge (multi-currency...) but will do

If it isn't already on the release plan, I think that it would hugely improve the product if there was a content module that could allow filtering formulas to be entered so that there is the ability to show all items in a category 'where <field> is <operator> than <value>' e.g. "where 'color = 'red'" or 'price > 300' and then 'sort by <field>' options

If someone wanted to write this as an extension...

It's in the todo list already.

Would it be possible to get an idea of how high up on the list it is and generally what the planned release schedule is?

thanks

Our schedule is already full for the next month with other things. We don't have any predefined roadmap after that but filters is not THE priority so it won't come before a few months I would say.