I can recommend the Hotel 81 chain. Most of their hotels are away from the centre, the rooms are very small, but it is good value for money. I stayed in Geylang Hotel 81 in Geylang, it is close to Aljunied MRT Station. The city centre is a 45 mins walk.
On my second visit I wanted a larger room and wanted to be closer to the centre and stayed in Bencoolen hotel in Bencoolen street. Bigger rooms than the 81 one hotels also more expensive. here are the websites
I've been to Singapore and I saw a couple of cheap hotels there. Maybe you try The Metropolitan Y Hotel Singapore, it is located in Orchard vicinity road, it cost around 70SGD.
I tried Hotel 81 Orchid Singapore before with my husband. We were with my kids and they enjoyed our stay there. It's pretty cheap but the accommodation is nice.try to check it out maybe it'll fine with you.
You already have some good suggestions. Hotel rates in Singapore have increased, I often find it is a good idea to look for some last minute bargain, http://www.asiaoz.com/ has a last minute section for Singapore with last minute availability where the hotels sell off their rooms cheap at the last minute.