I am glad to hear your family, and you are coming to Singapore for the holidays. I also heard that you are interested in learning about Singapore's cultural and modern aspects and sample some local dishes. Let me be your guide and take you around.
We can meet at 10 am in the hotel's lobby. First, we can go to little India, the most colourful districts in Singapore. We can see gaily painted shophouses selling traditional Indian apparel, gold bangles, spices and other wares. While the sun is up high, we can chill at the 24-hour shopping centre, Mustafa Centre, one of the few 24-hour shopping malls in Singapore. For lunch, we can eat fish head curry, a uniquely Singaporean dish.
We can then head to Chinatown and visit beautifully restored shophouses. Since you mention wanting to know of Singapore's culture, we can ride a trishaw around the vicinity and learn about its culture and history. We can bargain at its market for souvenirs.
For dinner, we can eat chilli crab, a unique local dish that cannot be found anywhere else. After that, we can visit the Merlion Park, a very modern place in Singapore. As the night ages, we can take a ride on the Singapore Flyer and enjoy a beautiful night view before heading back.
I hope to be hosting you soon. You will be guaranteed a great stay in Singapore.