I'd second the Hotel Julen. A very nice 4*. Good location in the middle of town but off the main drag. You should be able to get a late season rate there. It would be a nice reward after the Haute Route. 3* Hotel Cheminee is also a good option. Lower priced that the Julen. These are both smaller, family run hotels rather than big tourist package type hotels.
Good luck on the Haute Route; I hope your weather conditions cooperate. Having done it multipe times, it's still stands out to me as one of the most memorable skiing adventures that the average skier can do.