until mid-may , -lrb- 602 -rrb- 248-6000 ; from mid-may to mid-september , -lrb- 406 -rrb- 226-5551 . ; -lrb- check -rrb- mount rainier national park , washington -- glacier has the name , but you will see far more impressive glaciers on the slopes of 14,410 -foot-high mount rainier , and they are easier to get to .