Shakespeare actually used nice in several different senses:

These are complements, these are humours, these betraie nice wenches that would be betraied without these. Love's Labor's Lost [wanton]

And he that stands vpon a slipp'ry place, Makes nice of no vilde hold to stay him vp. John III [to display reserve]

That policie may either last so long, Or feede vpon such nice and waterish diet. Othello [thin]

The Letter was not nice, but full of charge, Of deare import, and the neglecting it May do much danger. Romeo & Juliet [trivial]

To set so rich a mayne On the nice hazard of one doubtfull houre, It were not good. Henry IV [critical]

Ile proue it on his body if he dare, Despight his nice fence, and his actiue practise. Much Ado.. [carefully accurate]

We will enjoy That *nice-preserued honesty of yours. Titus..

stupid/foolish > wanton/lascivious > extravagant > elegant > strange > slothful > unmanly > luxurious > modest > slight > precise > thin > shy > discriminating > dainty > pleasant and agreeable

"You scold me so much in a nice long letter.. which I have received from you." - Jane Austen

(what do you suppose she meant?)