I think just about any armorer can repair your magic armor, and a mage can recharge your magic weapons. During normal business hours, for a hefty price, of course.
Also, once you reach level 50 in armorer skill, you become able to repair your own.
Armorer Skill trainers: (hilight)
Low Level
Eitar: Leyawiin (Margarte's house E. of Chapel of Zenithar)
Tadrose Helas: Bravil Fighters Guild
Medium Level
Rohssan: Imperial City (A Fighting Chance shop in Market District)
Rasheda: Chorrol (Fire and Steel shop)
Master Trainer
Gin-Wulm: Imperial City (The Best Defense shop in Market District, or
wandering Market or Elven Gardens District)
* Quest