Whether either is correct depends on what you are trying to say.
If you write, "Sally looks good in her new dress", "good" is an adjective. The construction is similar to if you wrote, "The dress looks blue".
If you write, "Sally looks well", people would normally understand you to mean "well" in the sense of healthy. Again, "well" is an adjective.
You might conceivably say "Sally looks well" using "well" as an adverb to modify how she looks. In that case, you are saying that Sally is doing a good job of looking. Such a sentence might be used to describe someone who is acting as a look-out, for example. It would be a similar construct to, "Sally cooks well" or "Sally drives well". But frankly, it's a rather unlikely thing for someone to say.
A common mistake in English is to use an adjective when you should have used an adverb, like "I speak English good" when you meant to say "I speak English well." But don't be confused by this and think you should always use an adverb after a verb! "Sally looks good" is correct if the intent is to say that Sally is pretty or otherwise to be favored. (Should I clarify that "... looks good" is often used other than in the sense of personal appearance? Like, "Which of the people who applied for this job should we hire?" "I think Mr Jones looks good." The meaning is that Mr Jones looks suitable for the job, not that he is handsome.)