Python 3, score 5390.25, 998 bytes##bytes
I used a simulated annealing program to fit rectangles into the shape of Starry Night. Then it uses a Gaussian blur to smooth out the straight rectangular edges.
To save some bytes, I compressed the rectangle data into base 94.
from PIL import Image as I,ImageDraw as D,ImageFilter as F
def V(n,f,t):
z=0;s='';d='''0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ!@#$%^&*()_-+={[}]|:;"',<.>/?`~ '''
for i in n:z=z*f+d.index(i)
while z:z,m=divmod(z,t);s=d[m]+s
return s
i=I.new('RGB',(386,320))
K=V("""12XsPc/p^m(:,enp:SN8brwj%!iChDHKj"*445Z.;/8Xj408fV9a7:v$N#cj_WNW7p#t9:](i?S!}yg*D4u$RfpU=}=@Ft^v7$N5O?8eeN%.bT:Q>+AOd3E*R/1PXq.IO,ur3h<`dS)V;e/lj6q'p4s|m>fkk<!jx`EGU~38(0h!(I6P.<[G;m_c^x{kE^hYQUV9kIiS'T:GDRQz -ISW6@cLKz4!e&8LT]kH3'Hj=Zl]rEOyrXlmfG51.K1(5l{:GPb1PL5%.gMmLy;pU3h+zDxpSn@)nJ*#'EOt=Pt.t9z,;D.[r|Prpeu=0%WN+A~KSb(E:gd%o2QfB_K-!xLAN+jXicd**bk'WDq,ue&z]Rb>;DBCFif{zJEDfx3FKqB*?2Qti:(pYSa-uZU,M!^N =bRbZ`}j}P-u-n>lGH|pv>#r"}Eg&c6J&fi.IC@2:L""",94,10)[1:]
e=D.Draw(i)
for X in range(0,len(K),21):
y=K[X:X+21];x=[]
for z in range(0,21,3):x+=[int(y[z:z+3])]
e.rectangle((x[0],x[1],x[2],x[3]),(x[4],x[5],x[6]))
i=i.filter(F.GaussianBlur(radius=5))
i.save('2.png')


