A night without sleeping

I've always liked: "I had an all-nighter."

This generally refers to a night out on the town, night-time shift work, or cramming for exams. Something of that nature.

You have a choice: an insomnia, a sleepless night (the noun is sleeplessness), a wakeful night (wakefulness), a restless night (restlessness).

There is also the word fitful, as in "I had a fitful sleep last night," which means the sleep was intermittent and not restful, not a proper night's sleep at all.

Insomnia perhaps but you still need something like "I lay awake all night with insomnia" which is a bit redundant.