There's been quite a few questions about hawker stalls in Singaporein the past, I thought I'd summarize some of the strategies/rules of thumbs for finding the better ones.
Some of the best hawker stalls in Singapore tend to be the older ones, including those that have been handed down a generation or so. These are typically located in some of the older hawker centres or coffeeshops (a little more about hawker centres and coffeeshops later).
In other cases they may have moved, but will be relatively easy to identify -- they might have names that reflect their original location. So if you see a hawker stall with a name that's not reflecting it's current location, it's worth a try. Also worth looking for are hawker stalls that indicate that they were from elsewhere (e.g. "original stall from XXXXX") that's a sign (literally) that they are banking on a good reputation from a past location and are aiming to attract their ex-regulars.
Also, another useful clue is long lines at the hawker stall (Singaporeans epitomize chowhoundom) or a slightly older cook that operates fast -- it can be reflective of one that been around for a long time and used to dealing with a high volume.
Many hounds are familar with hawker centres -- structures with tens of hawker stalls under one roof. the less mentioned coffeeshops can be thought of as mini-hawker centres, they're home to maybe 6-7 stalls and tended to be more distributed. One is liable to find them on the ground floor of the houndreds of government-built hi-rises that house ~70% of the population as well as part of many residential estates.
Good ones tend to be the older ones, e.g. Hong Lim, Maxwell Road, Cuppage Centre and a bunch of others in or near the downtown or central business district. But many hawker centres in the residential neighbourhoods are likely to harbour great stalls too. I've been very fortunate with the ones in Bedok and Tampines, near where I live. I bet going out to other large residential nabes like Marine Parade, Yishun, Ang Mo Kio or Toa Payoh will pay off, be it hitting the hawker centres (there can be several) that serve those areas or scouting out the smaller coffeeshops. The more modern air-conditioned food courts at malls etc... can be very pleasant and delicious, but may not offer some of the definitive versions of hawker fare.
Of course these are just rules of thumb, and many exceptions exist. But it's potentially a useful start for chowhounding in Singapore i.e. going out on a treasure hunt for good places instead of relying on beaten paths.