I suppose at the end of the day for your visit it depends on what your total budget is. One website we discovered when we visited earlier this year is wotif.com.sg which has "mystery deals" on hotels. We got a 4.5 star hotel for $125sgd a night which was ok for us since we only wanted to stay 4 nights.
$2 to $5k pcm will definitely get you a condo
I'm about to move out to Singapore later this week - like you on a local terms contract for 3 years although I suspect that working for a bank is a tad more lucrative than my job if that's the sort of money you're talking about with no housing allowance!
I think you will find a hundred and one suggestions on where to live etc etc on these forums - many seem to suggest the East coast for somewhere less costly, many others choose to live in or close to the CBD for convenience.
Following my own recce I prefer the west since it's a little more out of the way and quieter - also for me, it's more convenient for work and I have a lot of family living that side.
The Bukit Timah area is popular with expats as far as condos
go, but nearby, there are the HDB estates at Clementi which from experience of staying with family there are pretty good and well kept.
If you're just going for a look around, I'd definitely try to "go local" and have a look around somewhere like Clementi. it's an area I know well, but I still think that compared with somewhere like Toa Payoh, it's "cosier" - not from an overcrowded sense but less "frantic" and easier to find one's way around the shops.