When thinking about beautiful things, I realized there was nothing for me to do but gaze at them in admiration.
Literal
Beautiful things [about-について] thinking [when-とき] I [to-には] gazing admiring thing other [to-に] self [to-には] nothing doing [subject-が] not-exist [quotative-ということが] understood [copula-のだ].
A reflective, philosophical sentence about the helplessness of beauty's observer. 見つめて感心すること以外には means 'other than staring and admiring.' わかったのだ closes with explanatory の + だ, marking a personal realization. Elevated written register.