I posted a rundown of singapore hawker centers some time back. You can take a look at the variety available.
At a glance, i would recommend a few outstanding places to eat (nvm the cleanliness):
1. Smith street
2. Maxwell food ctr
3. Tanjong Pagar Hawker Ctr
4. Tiong Bahru HC (Ex though)
5. Changi Village HC
6. Bedok Central HC
If you're looking for specific food items at specific places, i would highlight:
Nasi Lemak - Boon Lay Mkt
Chicken Rice - Boon tong kee at balastier
Duck Rice - depot rd (near mindef Manpower towers)
Porriage - smith/maxwell HC
authentic jap fd - Shima at gdwood park hotel (Tepanyaki), Chanko Masakatsu at Bugis Junct (jap steamboat)
when i think of more i'll let you know
