"what areas of nursing offer the most chances for this shift?"
Well, ANY facility that runs 24/7 needs weekend people. After you have gained a year or so experience, you will find many openings available, including agency work, if you like to work weekends.
I am no longer interested in doing so, but some advantages are:
1) having week days to do banking, chores, attending classes, getting car worked on, etc.
2) going to the movies, hiking, etc. during weekdays when crowds are not in the way
3) being paid for more hours than one works (in some cases)
4) scarcity of administrators and supervisors looking over one's shoulder (and freaking out under any and every kind of stress--imagined or otherwise)
1) if someone does not show up for work, there are few people to call to replace him/her (which can mean either "working short" or mandatory overtime, depending on the facility)
2) limited support functions ("oh, that department is closed on weekends")
3) a more limited social life.
My personal favorite is part-time or per-diem weekday evening shifts only, since I don't like to get up early.
To each his own, and since your preference is something that most people don't want to do, you have more options than you would have otherwise.