For any of the regular TS restaurants (1TS credit) regular park attire is just fine.
Victoria and Alberts specifies a dress code: Note: Proper Attire may include the following
Men: Dinner jackets with dress pants/slacks and shoes. Ties are optional (Please no jeans, shorts, sandals, flip-flops, or tennis shoes)
Ladies: Cocktail dress, dressy pant suit, skirt/blouse or nice dress. (Please no jeans, shorts, capri pants, sandals, flip-flops or tennis shoes)
The above was copied from the WDW restaurant site.
The info below is from the Citrico's (one of the signature restaurants) page. I believe most of the other signatures are similar:
Dress Code Guidelines:
Men: Khakis, slacks, jeans, dress shorts, collared shirts. Sport coats are optional.
Ladies: Capris, skirts, dresses, jeans, dress shorts.
Not permitted in dining room: Tank tops, swimwear, hats for gentleman, cut offs, or torn clothing. While T-shirts are now allowed, the policy remains that T-shirts with offensive language or graphics are not acceptable.
I hope this helps.