There were too many sights to see them all in a day or two.
Literal
Famous-places [subject-が] too many [and], 1, 2 day [in-で] see [go-わけ] can't.
あまり多くて = 'too many, and therefore.' The て-form chains the reason into the following impossibility. ~わけにはいかない ('can't manage to / it won't do to') is the standard 'I can't bring myself to / it's not feasible' expression. Often used for social, moral, or practical impossibilities.