Everson Mono works in PuTTY (a very important condition; many other fonts work, e.g. in konsole) for all the characters you posted. Doing a full test with the Python script, however, reveals a block that isn't quite right.
python -c 'print u"\u22c5 \u22c5\u22c5 \u201d \u2019 \u266f \u2622 \u260d \u2318 \u2730 " \
u"\u28ff \u26a1 \u262f \u2691 \u21ba \u2934 \u2935 \u2206 \u231a \u2240\u2207 \u2707 " \
u"\u26a0\xa0\u25d4 \u26a1\xa0\u21af \xbf \u2a02 \u2716 \u21e3 \u21e1 \u2801 \u2809 " \
u"\u280b \u281b \u281f \u283f \u287f \u28ff \u2639 \u2780 \u2781 \u2782 \u2783 \u2784 " \
u"\u2785 \u2786 \u2787 \u2788 \u2789 \u25b9\xa0\u254d \u25aa \u26af \u2692 \u25cc " \
u"\u21c5 \u21a1 \u219f \u229b \u267a ".encode("utf8")'
To use Everson Mono on PuTTY it may be necessary to tick the
Allow selection of variable-pitch fonts box in the
Font settings area.
Other fonts, such as DejaVu Sans Mono, work perfectly in other programs, possibly borrowing glyphs from other files (I'm not sure how TT fonts work), which doesn't seem to work in PuTTY. Code2000 should have worked, but it did something... odd... to my PuTTY window. It may work for you. Every font I've tried works directly in konsole, even those that should not. It might be worth looking into an alternative client/emulator.