Make the most of Kuala Lumpur, Bangkok and Singapore

The limestone Batu Caves I'm planning a two-week family trip to Kuala Lumpur, Singapore and Bangkok in late October/early November. We're thinking of travelling by train - how do we go about it and how many days should we allot per city? What are the must-see attractions? Can you recommend a few reasonably priced hotels?
The most scenic way to travel between the three cities is by train. The six-hour journey from Singapore to KL follows a single-track railway through palm estates and rural stations, with plenty of great views in between. The next leg is from KL to Butterworth in Penang, from where you catch a 24-hour train to Bangkok. As there's no such thing as a single train ticket from Singapore to Bangkok, you'll have to buy separate tickets: a second-class seat from Singapore to KL costs S$34 [Dh100]; 34 Malaysian ringgit (Dh40) from KL to Butterworth and 112 ringgit (Dh132) from Butterworth to Bangkok (second class sleeper). Visit www.ktmb.com.my to book. The entire journey takes 48 hours, leaving you with four days in each city - enough for a good lookaround.
In Singapore, stay on Sentosa Island if you're travelling with kids - the entertainment zone is also home to the Universal Studios theme park. Sentosa Resort & Spa (www.thesentosa.com) has double rooms from S$335 (Dh975) per night, including taxes. For a quieter stay, book a room at the Robertson Quay Hotel, which is close to the restaurants along the waterfront and perfect if you feel like a late dinner and a boat ride in the bay. From S$200 (Dh580) for a double room per night, including taxes. Things to do in Singapore include a spin on the Flyer (Ferris wheel), a night safari at the zoo, a visit to Jurong Park for interactive sessions with tropical birds, and a night out at Satay Street for all the grilled meat you can eat.
The best way to get around is by the hop-on, hop-off bus. A 24-hour ticket costs S$22 (Dh64) per person (the route includes 22 stops; buses go by every 25 minutes; www.viator.com).
KL may be synonymous with the Petronas Twin Towers, but you'll have to drop them from your list - the buildings have been shut down until December for renovations. Make for Petaling street instead; at the heart of China Town, it's famous for the shopping and street food. Also visit the Forest Research Institute (www.frim.gov.my); 20km from the city, it has rainforests, wetlands and trails. For an insight into Malaysia's Hindu culture, make a trip to the limestone Batu Caves, about 13km north of the capital.
The three-star Corus (www.corushotelkl.com) opposite Petronas has tidy double rooms from 284 ringgit (Dh333) per night, including taxes. Or pay a little more for a Paradise Cabana (from 353 ringgit [Dh415] per night) - it has a balcony that opens onto the pool and a four-poster bed.In Bangkok, make inquiries at your hotel front desk for reasonably priced tours of the city, including temple explorations and day trips to the ancient city of Ayutthaya. If you visit on the weekend, go to Chatuchak market (open Saturday and Sunday only) for an unrivalled shopping experience.
For a good night's sleep, check into the stolid, traditionally decorated Imperial Queen's Park (www.imperialhotels.com) off Sukhmvit Road, a five-minute walk to the Phrom Phong elevated train station (the quickest way around the traffic-choked capital). Double rooms cost from 2,209 Thai baht (Dh266), including breakfast and taxes. The chic Amari Atrium (www.amarihotels.com) has double rooms from 2,080 baht (Dh250) per night, including breakfast and taxes, and is located close to Petchburi subway station.