Problems that are hard w.r.t UGC-hardness of VERTEX COVER
Node-weighted multiway-cut is a problem to which vertex-cover can be reduced to in an approximation preserving way. Thus, a better than $2$-approximation for node-weighted multiway cut is not possible assuming UGC. The reduction was shown by Garg-Vazirani-Yannakakis in their paper which also established a $2$-approximation for node-weighted multiway-cut.