Hi Alison,
I spent about three weeks in Malaysia. I was on a round the world trip and I had a mate flying out to meet me for a two week holiday, so we packed in a lot in those two weeks - too much, in fact, it was too rushed - but I can recommend the following places:
Kuala Lumpur - worth a couple of days at the beginning and a day or two at the end, but I wouldn't linger. Apart from the Petronas Towers, KL has modern shopping and local markets, plush restaurants and great street stalls... real diversity. Its joy for me is the diversity of truly authentic food you can find. Little India is a must and will serve you up with wonderful veggie Indian food (although rarely alcohol, in my experience); equally you'll find decent and cheap Chinese and Malay grub all over the place. If I recall correctly here's a dim sum restaurant smack bang in the centre on Jalan Pudu that's worth a stop. I think someone on here (Emdee perhaps?) said there was something "missing" from KL that he couldn't put his finger on, and I wholeheartedly agree - it's not as good as it sounds on paper - but it's a decent place to adjust from the jetlag before pushing on into Malaysia.
Perhentian Islands - I absolutely fell in love with the Perhentians. I had never seen such clear, hot water and white sands. You can eat each day's catch on the beaches in the evening in the form of barbeques, go snorkelling/scuba diving to look for giant turtles and sharks. Not sure how it is five years on - I would expect it to be increasingly upmarket and developed, there's only one direction for these things - but I would love to go back and spend 4/5 days there doing very little but reading and sunning
Taman Negara - it's not every day you get to visit a teeming rainforest that has not changed in millions of years, so it's worth the journey I feel. There are "safari" tours to show you some of the wildlife, but the quality varies - get a personal recommendation. Even though there are tigers about, you're pretty unlikely to see one unfortunately.
Cameron Highlands - the cooler heights of the Cameron Highlands can be worth a stop, especially if you are a tea drinker (to see the plantations)

But it's quite a journey, and perhaps a bit too "Anglicised" to suggest to include on an itinerary for a Brit on holiday.
Sabah/Sarawak - I hardly touched the surface of these areas of Malaysia, but there are plenty of opportunities to find both R&R and culture. Kuching is a pretty city, and further into the jungle you can see orang-utans/visit the sanctuaries that protect them. The highlight of Malaysia for me was climbing Mount Kinabalu near Kota Kinabalu; it was a surprisingly easy climb for an unfit chap like me, although tougher on the final push. It's not every day you get to see the sun rise at 13,500 feet, and I'd absolutely recommend it to anyone vaguely interested :)
So as for an itinerary, I would tentatively suggest:
-1 week on the peninsula, in the form of a couple of days in KL getting adjusted then off to the Perhentians for 4 or 5 days of doing nothing (perhaps Taman Negara in between?)
-1 week in Sabah/Sarawak, visiting Kuching, then off into the jungle for a bit before heading to Kota Kinabalu to climb Mount Kinabalu
-Back to KL (perhaps via Penang for a bit more R&R?)
Can anyone else suggest an alternative itinerary with places to absolutely not miss in Malaysia?