You’ve posed a simple but strangely challenging question. Because Singapore is famously expensive for hotel accommodation—hotel rooms here bear comparison to those in touristy European cities, such as Venice, where a matchbox-sized room commonly costs from Rs 10,000 or so. Much rests on one’s definition of ‘affordable’, of course. The cheapest hotel rooms at reputable chain hotels, such as Ibis (ibis.com), start from about Rs 7,000. For this price, you’ll get a smart little room, frills-free but perfectly serviceable, but likely to be a bit of a squeeze for a family of three—and especially if one intends to stay as long as a week. Try the Santa Grand hotels; they have a variety of hotels, but the one at Bugis, for instance, offers very decent double rooms for under Rs 5,000 (santagrand.sg). Fragrance Hotels is another group of hotels that offers rooms for about the same price (fragrancehotel.com). The Little India neighbourhood has several small hotels that offer rooms of varying sizes and quality. Mayo Inn seems to be well-liked (mayoinn.com).
If all this doesn’t suit your idea of ‘affordable’, you could do worse than trying one of the smart hostels that Singapore abounds in. Yes, many are designed for the global backpacking community and, yes, most offer only dorm-style accommodation, typically with shared bathrooms. But that’s changing—families looking for inexpensive accommodation are now flocking to these hostels because many now offer private rooms in recognition of this demand. The webpage www.hostelbookers.com/blog/travel/family-hostels offers a useful primer on how to choose hostels. Rates at hostels start from approximately Rs 2,000. And one recommendation I can offer is Ark Hostel (arkhostel.sg). If renting a room in a private home is something you’re willing to consider, you could try your luck at airbnb.com—most listings offer rooms starting from about Rs 2,000 a night.