For a general algorithm for simulating points from a determinantal process, see Algorithm 18 in the paper "Determinantal Processes and Independence" by Hough, Krishnapur, Peres and Virag:
This algorithm was actually implemented by some physicists at Princeton (I believe) but I am not sure if their code is publicly available.
For the sine kernel, depending on how many points you want to sample, Matlab is pretty good at computing eigenvalues of a large GUE matrix in a decently short amount of time. That would require much less work than implementing the algorithm above.
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