Ah, that reminds me of a word I learned a while back - "Mądrala" (smartarse)
British English uses "smart" to mean "well-dressed". I'm guessing that you wouldn't use "mądry" to compliment someone on their nice new suit!
If you added some noun, thus creating a noun phrase ("smart woman", for example), then it would go into Instrumental and be "Nie jestem mądrą kobietą".
Don't know what nicole means by Nope. Eg. He is top of his class. Yes he's very smart. Meaning clever.