My favourite cut of beef is fillet. I think this should be everyones if they have ever had one cooked perfectly. It just melts in you mouth. Some of the options for this poll are braising meats anyway which you cant grill.

Beef fillet is proberly the hardest to cook as it doesnt have as much fat as some of the other cuts but just make sure you get it sealed in a hot pan (but not too hot as it will be dry) then finish it in the oven at 200 C. I dont like grilling meats anyway because if you havnt sealed the meat first you will lose a lot of the juices. Also you dont get pan juices which are essential for making a good sauce/gravy. I see people discard the pan juices and it is a total waste of flavour. When the meat is cooked take it out to rest then heat up the pan on the stove. Deglaze with wine (red for steak), then add stock and reduce by half. Check seasoning and you are left with the best gravy ever.