Penang and Kuching are a flight away and you would most probably spend most of the day in airports and on the plane rather than see anything if you plan for just a day trip. If you're planning a day trip to Malaysia, I recommend Malacca, and there should be buses that would drop you off in town and pick you up from there, your hotel concierge should be able to point out the bus companies. Otherwise some travel agencies in Singapore might have day tours to Malacca.
Another alternative is the beaches in Desaru in eastern Johor, and that is quite close to Singapore as well.