matplotlib -- interactively select points or locations?

You may want to use a pick event :

fig = figure()
ax1 = fig.add_subplot(111)
ax1.set_title('custom picker for line data')
line, = ax1.plot(rand(100), rand(100), 'o', picker=line_picker)
fig.canvas.mpl_connect('pick_event', onpick2)

Tolerance set by picker parameter there:

line, = ax1.plot(rand(100), 'o', picker=5)  # 5 points tolerance

from __future__ import print_function
import matplotlib.pyplot as plt
from matplotlib.lines import Line2D
from matplotlib.patches import Rectangle
from matplotlib.text import Text
from matplotlib.image import AxesImage
import numpy as np
from numpy.random import rand

if 1:
    fig, ax = plt.subplots()
    ax.set_title('click on points', picker=True)
    ax.set_ylabel('ylabel', picker=True, bbox=dict(facecolor='red'))
    line, = ax.plot(rand(100), 'o', picker=5)

    def onpick1(event):
        if isinstance(event.artist, Line2D):
            thisline = event.artist
            xdata = thisline.get_xdata()
            ydata = thisline.get_ydata()
            ind = event.ind
            print 'X='+str(np.take(xdata, ind)[0]) # Print X point
            print 'Y='+str(np.take(ydata, ind)[0]) # Print Y point

    fig.canvas.mpl_connect('pick_event', onpick1)

Wow many years have passed! Now matplotlib also support the ginput function which has almost the same API as Matlab. So there is no need to hack by the mpl-connect and so on any more! (https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.ginput.html) For instance,

plt.ginput(4)

will let the user to select 4 points.