She'll train anyone, but she's associated with the Thieves Guild, so if you're a member she'll have a higher disposition. Ganredhel: She's a Bosmer in the city of Cheydinhal. There are two advanced acrobatics trainers. SPOILER ALERT: During the Rats quest, your very first in the guild, talk to her after catching her red-handed, if you let her off the hook, talk to her again later to get free training. Bonus: If you're in the Fighter's Guide, you can get free training from her. If she's not at home, check The Count's Arms or Lelles' Quality Merchandise. Quill-Weave: She's an Argonian in the main Anvil section. If she's not in her house, look for her on the road to Chorrol or in the Arena where she gambles. Ida Vlinorman: She's an Imperial in the Elven Gardens District of the Imperial City. If you're in the Fighter's Guild, it's worth noting that you can get some free training out of Quill-Weave in the Rats quest.
One in the Imperial City and the other in the city of Anvil. There are two low level acrobatics trainers. Oblivion Power Leveling Guide: Acrobatics Trainers