You can fit quite a lot of plain text in 1kb; it's really just a 1024 character message. What you'd want to store would really be dependent on how the day went, but starting with "You are in a time loop. It resets every week on Monday at 6AM" would probably be sufficient to get things rolling; that's only 61B.
I'd just add information that helped me have the best 7 days possible - really just a schedule of things to do. Did I read a really good book? Note that down, read it every week, enjoy that time. Did I play a great game? Same thing. Once I found 7 days worth of activities that were maximally enjoyable, I'd be happy to just stay in that time loop forever; the memory reset is really a blessing, not a curse.