I went to bed at 2 a.m.

Both "I slept at 2 a.m." and "I went to bed at 2 a.m." are grammatically correct, but they may imply slightly different things.

"I went to bed at 2 a.m." is probably more commonly used, as it means that's the time you actually retired to bed, but it doesn't indicate if you fell asleep immediately.

"I slept at 2 a.m." suggests you actually fell asleep at that time, but it's used less frequently because it's rare for people to know the exact moment they fall asleep.
  
So in everyday conversation, you're likely to hear "I went to bed at 2 a.m." more often.