I can recommend Ellisland Farm. We were given a very comprehensive tour by the curator. This man is so knowledgeable, and obviously has a great affection and admiration for Robert Burns. The collection has some interesting pieces actually owned by Burns himself, and there are great walks around the farm itself.
Burns' House in Dumfries is to be recommended for its very helpful staff, and is a great small exhibition, full of information. We thoroughly enjoyed both visits.