Do you need absolute resolution. I made an anemometer with an arduino but not direction. If you didn't need perfect direction could you not use a series of Hall effect sensors and display the last trigger as the direction. I appreciate this is only an approximate direction but would be good enough for N, NE, E, SE, S, SW, W, NW display with 8 sesnsors. Sorry, probably a silly too simplistic suggestion but thought I'd mention it!
I struggled calibrating mine, have you considered this yet? I ended up with an arbitrary wind speed value which day by day was comparable but struggled to calibrate it with actual wind speed.