Who will buy fine clothing?
Solution 1:
Any general goods merchant (signage usually consists of a balance scale), spell merchant (typically a court wizard or one of the instructors at the College of Winterhold), and Radiant Raiment in Solitude (signage shows a needle with thread) will purchase both fine and common clothing, according to UESP.
For very early players, the Riverwood Trader is probably one of the more convenient options. You could also sell to Belethor's Shop in Whiterun, or Farengar Secret-Fire (the court wizard of Whiterun, who you will meet as part of the main quest).