I am looking for character which could replace image icon, for example like ✘ (xmark) and ✔ (tick), maybe some symbol to \"draft\" or \"new message\"?
EDIT:
To find useful symbols, I have two great resources:
Allows you to draw a shape, which it then searches for similarly shaped unicode symbols.
Lists unicode by the character blocks (using an embedded unicode font to maximize compatibility for display) and has a "display a certain block with images" functionality that allows you to review symbol blocks.
Both are quite useful though I often end up using shapecatcher these days just because it's a fun break just to be able to draw the shape that you want and have the site pull it up for you. At least, sometimes it will put it up.
http://shapecatcher.com/unicode/block/Miscellaneous_Symbols_And_Pictographs is also a great category of unicode symbols, though as with all unicode, you may have to test compatibility.
https://www.fileformat.info/info/unicode/block/miscellaneous_symbols/images.htm is the block of the miscellaneous symbols, for comparison.
Are also good symbols to add to the list.
Edit: In 2019 I would now recommend using a robust icon pack, either in svg form or font-file form, the presentation of unicode is often less controllable for web developers.