In reply to riojaiv:
We've slept and acclimatised at all three recently. They are all friendly and well run.
The Weismiess is super-accessible, take the lift and either walk up or down (depending on where you get off). Or slog up from Sass Grund, prettily. The warden is well worth discussing your plans with. Lovely man.
Almageller has a v pretty Alpine walk with suspension bridges and you can have lunch at the Almagelleralp hut on the way. Or walk over from the Weismiess hut to get two nights up high.
Our first two days this year were an acclimatisation trip to the Britannia (the highest) which I'd highly recommend. Bus to Mattmark, walk glacier trail from the lake up to the hut (usually v doable solo but ring hut to check), night at over 3000m, next morning do the via ferrata - they hire kit - and any scrambling you fancy, then beautiful traverse to Plattjen lift back to Saas Fee. (Check the lift down is still working, I don't think it is every year.)
Haven't been in early season for ages, but last year no probs booking the night before in September, except at weekends.
Have fun.