5 deleted 4 characters in body
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Python 2, 151150 bytes

S,N=input()
X=y=n=0
Y=x=c=-1
s=eval(`[[' ']*S]*S`)
exec"if n%S<1:S-=c%2<1;X,Y=-Y,X;c+=1;n=0\nx+=X;y+=Y;s[y][x]='*';n+=1\n"*N
for i in s:print''.join(i)print`i`[2::5]

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Python 2, 151 bytes

S,N=input()
X=y=n=0
Y=x=c=-1
s=eval(`[[' ']*S]*S`)
exec"if n%S<1:S-=c%2<1;X,Y=-Y,X;c+=1;n=0\nx+=X;y+=Y;s[y][x]='*';n+=1\n"*N
for i in s:print''.join(i)

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Python 2, 150 bytes

S,N=input()
X=y=n=0
Y=x=c=-1
s=eval(`[[' ']*S]*S`)
exec"if n%S<1:S-=c%2<1;X,Y=-Y,X;c+=1;n=0\nx+=X;y+=Y;s[y][x]='*';n+=1\n"*N
for i in s:print`i`[2::5]

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4 deleted 8 characters in body
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Python 2, 153151 bytes

S,N=input()
X=y=n=0
x=Y=x=c=-1
Y=c=1
s=eval(`[[' ']*S]*S`)
exec"if n%S<1:S-=c%2<1;X,Y=-Y,X;c+=1;n=0\nx-=X;y-=Y;s[y][x]='*';n+=1\n"*NX;c+=1;n=0\nx+=X;y+=Y;s[y][x]='*';n+=1\n"*N
for i in s:print''.join(i)

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Python 2, 153 bytes

S,N=input()
X=y=n=0
x=-1
Y=c=1
s=eval(`[[' ']*S]*S`)
exec"if n%S<1:S-=c%2<1;X,Y=-Y,X;c+=1;n=0\nx-=X;y-=Y;s[y][x]='*';n+=1\n"*N
for i in s:print''.join(i)

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Python 2, 151 bytes

S,N=input()
X=y=n=0
Y=x=c=-1
s=eval(`[[' ']*S]*S`)
exec"if n%S<1:S-=c%2<1;X,Y=-Y,X;c+=1;n=0\nx+=X;y+=Y;s[y][x]='*';n+=1\n"*N
for i in s:print''.join(i)

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3 deleted 6 characters in body
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Python 2, 157153 bytes

S,N=input()
X=y=n=0
x=-1
Y=c=1
s=eval(`[[' ']*S]*S`)
exec"if n%S<1:S-=c%2<1;X,Y=-Y,X;c+=1;n=0\nx-=X;y-=Y;s[y][x]='*';n+=1\n"*N
print'\n'for i in s:print''.join(map(''.join,s)i)

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Python 2, 157 bytes

S,N=input()
X=y=n=0
x=-1
Y=c=1
s=eval(`[[' ']*S]*S`)
exec"if n%S<1:S-=c%2<1;X,Y=-Y,X;c+=1;n=0\nx-=X;y-=Y;s[y][x]='*';n+=1\n"*N
print'\n'.join(map(''.join,s))

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Python 2, 153 bytes

S,N=input()
X=y=n=0
x=-1
Y=c=1
s=eval(`[[' ']*S]*S`)
exec"if n%S<1:S-=c%2<1;X,Y=-Y,X;c+=1;n=0\nx-=X;y-=Y;s[y][x]='*';n+=1\n"*N
for i in s:print''.join(i)

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    Post Undeleted by Erik the Outgolfer
2 added 10 characters in body
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    Post Deleted by Erik the Outgolfer
1
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