ok, at 22 I’d go for student-land: Headingley, Hyde Park, Burley, Kirkstall; Horsforth or Bramley at a push as they’re still on the train lines; any further out is for when you’re older like me & want a quiet life 😉
However, studentland is very heavily subscribed & probably over-priced because of that…
south of the river means Holbeck, Hunslet, Beeston, none of them particularly nice places to live;
east side of town not nice at all (I’m from East Leeds Irish stock, grandparents lived in that part of town, not somewhere I’d want to go back to);
west = Armley, Wortley, Bramley & heading out towards Pudsey & Bradford. Having lived in the latter from 1982-98 I’d say avoid anything with a BD1-BD9 postcode, although parts of Wrose, Eccleshill & Idle (BD2) are ok