EDIT 5 June 2017: apparently this laptop uses the eDP display interface meaning it IS possible to put a different display into the laptop. Here is a reddit post with what display to buy: https://www.reddit.com/r/chromeos/comments/5p1z4k/just_upgraded_my_c720_screen_to_ips_and_it_was_a/
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all credits to joe who answered this but i thought I'd edit my answer because it is the accepted one.
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Typically screens for laptops are made for that specific model, and unless your screen is somehow defective you cannot get a better quality one for your laptop. A antireflective screen protector may help though.
Typically screens for laptops are made for that specific model, and unless your screen is somehow defective you cannot get a better quality one for your laptop. A antireflective screen protector may help though.