By "that region" do you mean near Singapore or Malaysia in general?

I was thinking more in terms of Malaysia or anywhere in the Region that could be reached by a reasonable short flight (an hour or two) or other means of travel.

My 2 favorite places are Penang which can be gotten to by train. And the Malaysian part of Borneo.

In Penang I absolutely loved staying at the Cheong Fatt Tze Mansion. And then there's the Eastern & Oriental. And beach places to stay.
www.cheongfatttzemansion.com

In Borneo I particularly enjoyed the small city of Kuching. Then there are the orangutans, huge rivers, a mountain park, on & on.

Thanks, I will take a look at those locations. Since my wife isn't crazy about flying, it sounds like the visit to Borneo would be the only one requiring a flight. The train idea sounds great for Penang.

You may know this already, the island is Penang, the city is Georgetown. The train goes to Butterworth which is across a bridge from Georgetown.

Thanks. From what I am reading, it sounds like while it may rain often in Penang that time of year, but does not usually last all day. It definitely sounds like a great place to visit. Do you think it would be worth trying to stop in Kuala Lumpur either coming or going from Singapore to Penang?

Many people like KL, I don't. But since you'll most likely need to change trains there you might like to see which side of that fence you reside. Last time I was there there was a new Hilton right at the train station. I enjoyed staying there.

I am one of those that like KL. IMHO it has the best and most varied food in SEA from excellent and affordable upscale restaurants to small street stalls and "banana leaf" restaurants. There are some amazing hotels and the mix of cultures makes for a lot of variety in architecture and sights to see. Definitely worth a couple of days.

September is not rather best time of year weather wise for peninsular Malaysia, particularly on the east coast. If you want beach time, then the west coast has better weather at that time of year.

Otherwise, I tend to agree with MmePerdu. Penang is great for a few days as is Malacca. Bus travel is a comfortable and efficient alternative to flying for short/medium distances. The train journey from Singapore to KL is a nice alternative to flying. Some photos and more info on our last visit to Malaysia on our blog:
http://blog.travelpod.com/travel-blog/candcthai/1/tpod.html
Entries for Malaysia start at #20

You have gotten some good advice. In your position, I might take one of the luxury buses from SIngapore, stop in Malacca for a day or two, then take the bus to KL, then on to Penang. I'm not a fan of KL either, but it is worth a couple of days. I would spend the most time in Georgetown area of Penang.

If you do opt for a couple of days in KL, rather than staying at the train station, stay in the "Golden Triangle area" which puts you walking distance to shopping streets, food stalls, restaurants, etc. There is a JW Marriott, a Ritz Carlton, a Westin and a number of other hotels in this area.

In Penang, we loved the E&O Hotel.

The thing with Pinang is that you won't see any wildlife there. In fact, in the entire west Malaysia it is very difficult to spot wildlife. For wildlife you need to travel to east Malaysia (i.e. Borneo), for instance to the area near Sandakan where there are a few spots (Sepilok for orangutans, Labub bay for proboscis monkeys and the Kinabatangan river for wildlife in general). See here for more information:
http://www.molon.de/galleries/Malaysia/Sabah/

For beaches head to the east coast of peninsular Malaysia, which has much better beaches and much cleaner seawater than the west coast. I'd recommend either Perhentian or Redang islands:
http://www.molon.de/galleries/Malaysia/IslandsBeaches/

Getting there overland is possible (bus/taxi to Kuala Besut for Perhentian, Merang for Radang), then boat to the island.

FYI Amin, Penang has a large botanical garden with loads of monkeys including, according to Wikipedia, long-tailed Macaques and Dusty Leaf Monkeys and Black Giant Squirrels plus insects and butterflies that are wildlife too.

No question, if they want to see wildlife they need to go to Sabah. I don't recommend the "rehab" centers like Sepilok, but recommend the Danum Valley where the wildlife is truly wild. However, the OP said clearly they wanted to avoid flight, so Sabah and Sarawak are out .