Hi sirroma
I actually have my own 25 pages blog on Malaysia which is available to view. But I am not sure if this goes against the rules for posting a reply to you and giving the link. H'ver, in a nutshell, Malaysia has all that you want to see and do. There is Kuala Lumpur the vibrant capital with its colonial past, heritage buildings, a blend of the old and new. You can watch first class entertainment at KLCC, also go shopping there and anywhere around the hotel belt at Jalan P.Ramlee and Bukit Bintang.
You may be able to catch the Chinese New Year (CNY is on 26.01) mood at Petaling Street, known as Chinatown and nearby the Central market has local arts and crafts and food for you to taste. Food is cheap. You get a good and decent local meal for US3-5 inclusive of drinks. Even the fast food chains are relatively cheap. Budget accomodation are plentiful as well as 3 - 5 star hotels. Novotel is good and reasonably priced besides being central. If you're here around early Feb 09, you may join the Thaipusam celebration. A must watched Indian festival at Batu Caves. Info can be got at Malaysia's Tourism centre at Jln Ampang , Kuala lumpur.
You can travel down south to Melaka for this UNESCO heritage site with Dutch buildings, Portuguese fort and quaint Dutch influenced Chinese houses at Heeren St. Up north Penang has the beaches, and similar Heritage buildings and you have to try the food as it is the food capital of Malaysia. Also has a National Park for hiking, tropical fruit farm, Butterfly farm , a must see Peranakan museum and Cheong Fatt Tze museum.
Taman Negara is the place for jungle trekking and tropical rainforest in Pahang. There is also the beautiful Tioman Island off Pahang, Club Med at Cherating, Teluk Chempedak for your sailing, surfing, snorkeling.
Endau Rompin another State Park.. untouched wilderness, variety of fauna and flora, waterfalls, majestic rock formations.
Other beaches are Langkawi off Kedah, Pulau Redang, Pulau Perhentian and many others to choose.
You can take a coach from Singapore to Melaka, stop over for a day or two. Continue your journey to Kuala Lumpur by coach. Stay a couple of days and journey to Penang by train, cross over by ferry to Penang Island or take a direct flight. This way you do get to see the country from down south to up north. This much I can fill in for you. Kindly log into Tourism Malaysia's website.