I was sleeping fairly well about ten days into sobriety.
The fog took awhile longer, I was really hazy the first week or two, so even though I felt very good I had some problems putting together sentences and remembering words, I had a lot of "tip of the tongue" moments. Maybe 3-4 weeks or so?
A month sober is probably a good self-assessment milestone. I think by then you will feel pretty good, in comparison. You might think about keeping a daily journal, for a number of reasons I won't get into unless someone asks me.
I am at seven weeks sober, tomorrow, for reference.
Good luck