It depends a bit on your condition for hiking and your budget. Also, are the four days fully available for your hike, i.e. do they not include the approach and/or the departure trips?
Val d'Anniviers is better equipped with hotels and tourist facilities. Val d'Hérens (which I am more familiar with) is more "typical", e.g. if you want to hike away from the crowds and shoot nice photos. Hotels are available, but some are modest in terms of comfort.
I have three proposals:
1. Start in Vercorin (to be reached from Sierre by postal bus and cable car). Various hotels there, I don't have personal experience. On the first day hike to St-Martin (Accommodation at Pension Pas-de-Lona in Eison, no personal experience). 2nd day hike to La Sage (accommodation at Hôtel de La Sage, I have been there, it's a nice one). 3rd day hike to Arolla (accommodation at the Kurhaus, I have been there, very nice "Belle époque" mountain hotel, if budget is no constraint... Otherwise there are other hotels in Arolla. Oops, that's only three days, but you can modify using the link I give below. Such as hiking back from Arolla to Les Haudères via the very scenic Lac Bleu.
2. You can also visit both valleys, if you are fit to cross the Col du Torrent pass. In September it should still be snow-free. I suggest two days here, add whatever you want before Zinal. Once you are in Zinal (sleep there, many options available), hike to La Sage via Col du Torrent. You will see the Lac de Moiry reservoir, very scenic. Stay in La Sage as mentioned above. The next day hike to Arolla as described above.
3. If you are in excellent condition and don't insist on comfort, you could hike day one from Nax to Cabane des Becs de Bosson (that's an Alpine Club "hut", sleep in dormitories, bring a cloth sleeping bag, blankets available, I have been there). On day 2 hike to La Sage, on day 3 to Arolla as described above. If you are willing and able to do that, it would be the alternative providing the best memories!
Check out the SwitzerlandMobility website : www.wanderland.ch/en/s uisse-a-pied.html
Get familiar with this site, first make sure you are on the hiking pages (not cycling, canoeing etc.). Then go to the Map. Zoom in as you like. The hiking trails appear in green. For some trails, additional information is provided when you click on them. The Zinal to La Sage trail is called Alpine Passes Trail Stage 19, and La Sage to Arolla is Stage 20 of the same. Nax-Becs de Bosson-La Sage is Tour Pédestre du Val d'Hérens Stages 2 and 1.