Guten Morgen und herzlich willkommen im Forum
D 6/7 is like City Hall/Beach Road area I think.
Are you on your own? $4k will get you a
condo with facilities with easy commuting distance. Try do a search via this site using the site above, or on Google.
To be honest I was about your age when I first worked in SG. I lived on Mt. Sophia and I remember going to Dan Ryan's (top end of Orchard Road) one night and it feeling WAY out of my geographic comfort zone, that was how parochial I was. But the point it, you're young, you will be working very hard, long hours, what might matter more is proximity to a decent mall/supermarket and food-court. Then come weekends, well judging by your nice housing allowance I expect taxis to and fro from your salary will be no problem. So my point, you don't need to pay a big premium to live right 'in the centre'.
p.s. If you revert pls mention if you are coming alone, maximum commute time, and if possible be a bit clearer on work location (being on a direct MRT line or bus route from near home to near your workplace cuts out a lot of hassle, especially over the course of three years!)