Travelling Salesman and Planar Travel - Generalized TSP
If the tour is required to visit one node in each group, then the problem is called Group-TSP, or TSP-with-neighborhoods. There's a ton of work on this in the plane (just google it), and in general it's as hard as HITTING SET (the case in which your metric is all 1s). There's a paper by Safra and Schwartz that shows that Geometric group TSP (in the plane) is hard to any constant factor.