Actually, I found several websites offering similar services but they have less features compare to Street Directory:
1. Google Map
You might notice that Google map is not localized to Singapore as the default location is US. If you want to search a location in the country, you need to append the keyword location with ", Singapore" as shown below:
2. Can.com.sg
If you want to go by postal code or more detail search query, you may visit can.com.sg. This website also provides information such as nearby ATM/bank locations, Shopping centers and many public service facilities.
Even though the website also offers point to point public transportation guide, I prefer to use Transitlink's Bus Journey Planner as it provides more accurate bus stop location as well as bus service number.
Happy travelling in Singapore!