Would average commoners on the streets of cities throughout the new country have known who he was, and his contributions in the war?
Or would he have been known primarily to wealthy men of means, commanders in the revolutionary army, and the men who directly served with or under him?
As a somewhat related question, did Lafayette's service in the war have any impact from what we can tell on early American impressions of France, beyond just what general French support during the war would have done?
By the end of the war, I think it's safe to say Lafayette would have been as well known as a lot of other prominent figures. Not only did he become a personal friend of Washington (viewing him as the father he never had), Hamilton, and later Jefferson along with other founding fathers, but he and his wife Adrienne played host to many Americans visiting Paris. Abigail Adams mentioned the Marquise de Lafayette as being one of the few people she would be sorry to leave behind in France.
There were places named La Fayette, Lafayette or Fayetteville in his honor, just a few years after the war ( http://www.northcarolinahistory.org/commentary/125/entry ) Along with several instances of man who had served alongside him naming a child in his honor. In addition, Lafayette often provided letters of introduction for French travelers to America.
Though there was certainly anti-French sentiment in the colonies, due to English influence, along with the more immediate, personal recollections of the French and Indian war, I'd say American attitudes toward France were mostly favorable in the decade or so that followed American victory. Though the later tumult of the French Revolution, followed by the Napoleonic war, would put a strain on Franco-American relations.
One good biography (and my source for most of the above) is Harlow Giles Unger's "Lafayette". Though some scholars feel Unger casts his subject in too favorable a light. For a slightly more academic approach you may want to try "Lafayette in Two Worlds" by Lloyd S. Kramer. In addition, "Mémoires, correspondance et manuscrits du général Lafayette" are available in varying forms on Google Books.