multDist=MultinomialDistribution[1,{1/4,1/4,1/4,1/4}]
XYstep={{1,0}, {0,1},{-1,0},{0,-1}}
TwoDRW[n_]:={
Z=Table[RandomInteger[multDist,1][[1]],{j,1,n}];
Y = Table[Sum[XYstep[[i]]*Z[[j,i]],{i,1,4}],{j,1,n}];
YY = Accumulate[Y]; 
(*{Z,Y,YY}  *)
YY}
RW=TwoDRW[500][[1]];
ListPlot[RW,Joined->True]