I can't sleep, so I'm just staring at the clock.

Literal

Sleep-can-not [because-ので], I [topic-は] just clock [object-を] am-staring-at.

ただ ('just, only') combines with ~ている for 'just doing nothing but X.' 眺める ('to stare at, to gaze at') is more passive than 見る. A poignant insomnia scene.