The journey from KL to Singapore can be an excellent trip, even better if you do it from Chiang Mai in Thailand all the way down to Singapore. Glorious beaches, temples and sights galore and some of the friendliest people on earth. I've done similar trips twice now.
You say about 'just packing a bag and going', I've got to say I love your attitude! Travel, accomodation and general living is so very cheap, the only thought you need before you go is the places you might like to try. If you don't follow a prescribed plan you'll find the area all the more wonderous. Let me know how you get on!
As far as Indonesia is concerned, you may want to check with the FCO as they are more than likely warning off going at the moment, making Insurance very hard to negotiate a good deal.
Visited KL, Pangkor, Penang and Singapore last year. Malaysia is cheap (food stalls VERY cheap and good food), roads are excellent standard and the people are friendly. KL is a great city with plenty to see and do - a mix of modern and traditional side by side.
The airport is a long way from the city (40ish miles). If you buy an air ticket from the UK to KL you may be entitled to a free flight to another part of Malaysia or the far east with Malaysian airlines as part of the deal - ask the agent when booking as they often won't tell you!
Well, if you're going to Malaysia and enjoy some hiking etc, I do recommend going to Kota Kinabalu In Sabah. It's the higest mountain peak in South East Asia apparently. Alternatively you can also visits the caves in Sarawak, which has the biggest caves in the world. Both has some fantastic scenery and it's a great experience.
In terms of food, both Indonesia and Malaysia has a HUGE variety of food with a fushion of Malay, Indian and Chinese food. The best way to really enjoy them though is to know where to go. And sadly for that you;d really need someone who knows the area well to know where all the best stalls/cafes/restaurants are
One of my best food experience was in Penang, was literally eating 6 meals a day there with local friend showing me where the best places were.
Spent 3 months in Indonesia in 1991. It is one of my favourite countries. I particularly enjoyed Borabadour and Perambanen (don't know if I have speelled that corretly). Also Yogyakarta is a nice place to spend time. I did a batik course there - it is apparently their cultural capital.
Jakarta is really filthy and nasty but the rest of Indonesia is beautiful.
Malaysia is a great place to visit. I went to the rainforest in Taman Negara. If you go to the tourist office near the train station they can arrange transport and accommodation for you.