What time does sound good to you?
What time sounds good to you?
Is there a difference?
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With ordinary sentences we distinguish questions from statements by flipping the subject and the auxiliary verb (Subj/Aux inversion), and if there is no auxiliary in the statement form, we bring in do to serve the auxiliary function (Do support):
This time has been very pleasant →Q: Has this time been pleasant?
This time seems good to me →Q: Does this time seem good to you?
But when you ask a question using a wh- word as the subject, or as a determiner on the subject, the wh- word is what tells your hearer that this is a question; there is no need for Subj/Aux inversion, and therefore no need for Do support either:
This time sounds good to me →Q: What time sounds good to you?
As snailboat points out, does can be used to emphasize contrast with a prior negative:
A: Shall I put us down for the seven o'clock show? B: No, I don't much care for seven.
A: Well, what about two o'clock? Does that sound good to you?
B: No, two's no good for me.
A: (exasperated)Then what time does sound good to you?
If "who/what" or "what/which+noun" is the subject you don't use the question form with to do. So sentence 1 is wrong and sentence 2 is correct. http://www.englishgrammar.org/subject-object-question/
Who goes there? Who has done it? Who said this?
What is it? What's the matter? What makes the Earth turn round its axis?
The first sentence sounds wrong. The second sentence is fine.
But the following sentences that use "does" are correct:
What time does the train arrive?
What time do we eat?