Interpolate new point in a xy plane of data

I have a large xy plane of data with ~26000 points. The points are not in a
rectangular grid.
I would like to interpolate to a new point within this dataset. Is there an
easy way to do this?

I have tried interp2d, but it does not give me a valid result, e.g.

from scipy.interpolate import interp2d
in2(R[0],Z[0]) = [ 0.310331]


And I get this warning:
   Warning: No more knots can be added because the additional knot would
    with an old one. Probably cause: s too small or too large a weight
    to an inaccurate data point. (fp>s)
  kx,ky=1,1 nx,ny=4,282 m=26328 fp=1195.252616 s=0.000000


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