There is a popular category widget you can use on the homepage, however it is not specific to the location of the site visitor. The search box is as you see it on the
demo, however there have been improvements to the search in this next release as well (detailed in the link below). For the specific setup you have described, it would require some customization of the default theme.
You can find more specific information about what is available in the v1.1 release here on our
latest blog post, and in the release log also linked from that page.