All the suggestions below, in good weather, give great views of the 5 4000m peaks that cap this beautiful valley: Bishorn 4153m, Weisshorn 4506m, Zinalrothorn 4221m, Obergabelhorn 4063m and Dent Blanche 4357m.
If you want to try them yourselves, running or walking, please remember these are just our experiences and a good map, suitable equipment and weather are needed. It is also possible to extend all of the routes, either by returning down the same way or adding on a little more if you like.
1) Moiry Barrage to Corné De Sorebois (2895m)
Catching the incredibly convenient Postbus from Grimentz to the Moiry Barrage at 2250m makes this ascent to the stunning Corné De Sorebois very accessible. The route leads straight of the car park and is well signed to the Corné. With the gradient steepening toward the top this is a tough climb but, once there, the views over the entire Val d'Anniviers are spectacular. Plus, running back down to Moiry isn't necessary since a cable car runs from Sorebois right back to Grimentz. Both the bus and cable car are included in the summer Liberte pass too making it incredibly inexpensive too. It is also possible to do this route direct from Grimentz (1550m) by heading up to the barrage on foot first making for more than 1300m of uphill.
2) Moiry Barrage to Scex De Marenda (2906m) and Bendolla
Again start by catching the bus to the Moiry Barrage, but this time instead of ascending directly from the car park cross the impressive barrage first then start climbing up the opposite bank. The route then climbs steadily on obvious trails to the Alpage de Moiry where signs direct you towards the Scex de Marenda. Much of this route is on shallower tracks so a little easier going and the views over Lac Moiry to the Glacier Moiry are stunning throughout. After a final steeper section you reach a col overlooking a plateau with Lac de Lona, then turn right up to the summit of Scex de Marenda. It might seem tempting to skip the top and continue on instead, but if you can go up then do as the views from the summit ridge are unrivalled. Later, back at the col, proceed to cross the plateau to the Lac de Lona and veer left following signs to Bendolla. The descent is a little rocky but easy to follow. Bendolla cable car station at 2130m can then carry you back to Grimentz (unless you really want to run down of course).
3) Bendolla to Roc d'Orzival (2816m)
This time catch the cable car straight from Grimentz to Bendolla and pick up the signs to Roc d'Orzival which is basically directly ahead of you in line with the cable car. Alternating between hiking trails and 4x4 tracks this is also quite easy to follow and often gives a choice between a longer track or short, steeper trail as you prefer. Close to the top is a col with a viewing station close on your left, but if you can then bear right to the summit to enjoy brilliant views over the head of the Grimentz and Zinal valleys and even the Matterhorn beyond. Retrace your steps back to Bendolla for a ride home. You can, of course, also do this route direct from Grimentz and add an extra 600m of ascent/descent if you like.
4) Bendolla to Cabane Becs de Bosson (2983m) via Pas de Lona
Again starting out with a cable car to Bendolla and following the same initial route as Roc d'Orzival, but this time bearing left to follow signs to Cabane Becs Bosson. Once above 2500m the path starts to get a little rockier and even in summer can have a dusting if snow on it as it is on the north face of the slope. The final ascent to the col is pretty steep but once over the final approach to the Cabane is flat and gives awesome views of the mountains at the valley head. Once at the Cabane you could retrace your steps, or continue down to Pas de Lona and follow signs to Bendolla, covering much of the same descent route as from Scex de Marenda.