Short answer: Dover.

Long answer:

    In the actual city of Ann Arbor, I'm afraid there is nowhere to buy traditional riding clothes. Or boots. Just outside of the city, at Lakeside Saddlery, you can find Tuf-Rider boots and economically priced helmets, but as for the higher end, there are no alternatives to online shoping. That said, if you're just schooling or hacking, you can get away with clothing that's not specifically designed for riding. Try these places:

Bivouac (State Street, Ann Arbor)

I've been shopping here for so long... You won't find traditional riding apparel here, but you will find a bewilderingly large selection of technical clothing which is perfectly suitable for schooling (combined with your existing breeches and boots), hacking, or barn stuff. 

Lulu Lemon/Athletica (Most larger stores, and on Stadium in Ann Arbor)

Clothing designed for Yoga can be used for riding (again, combined with your existing breeches and boots). Close fitting, stretchy stuff in technical fabrics won't flap around in the breeze when you're cantering and jumping.

The Painted Trout (Dexter)

Equestrian "Lifestyle" clothing can also be used for riding (Duh). They've got the best of my favorite brands --Dubarry and Barbour-- and technical pieces from Patagonia. Dubarry's hacking jackets can even be used for shows.

But, I'm sorry to say, for the most traditional and high quality riding apparel, you'll have to venture out of Ann Arbor.