Is there a site that would allow you to search for "arrow", for example, and provide all the Unicode symbols that match the keyword "arrow"?
This would be very handy :)
Ideally, it would also show the Unicode symbol rendered as an image for users without the requisite fonts who would otherwise see these chars as squares.
http://tools.scarfboy.com/unicode.html is awesome. It has an intelligent box that guesses what you mean, shows which encodings can correctly encode the character, and more!
(It does assume that the right fonts are installed, though... no server-side rendering.)
This site seems to be what you're looking for, and for example this query to it shows a table with 500+ lines (unfortunately some duplication of code points, as each code point is multiply found if it has multiple definitions containing the text "arrow").