Please lah! Of all places to recommend.... DO NOT WASTE your rare weekend to dive in Singapore waters. Take the time to do a short weekend trip as recommended by the others to the 3 possible destinations, Pulau Tioman, Pulau Dayang or Pulau Aur. Dayang and Aur are essentially the same, sister islands less than 500m(?) apart, so the sites are pretty much the same sites.
Late March is pretty much the start of the season, so there'll be a frenzy of operators from Singapore going out to these islands. Dayang and Aur tend to be pretty much back-to-basics operations irregardless of which operator you choose to go there with as they use the same resorts. 4hr mini-van ride from Singapore at 8pm + another 4hr bumboat ride to the islands. You get into the islands at about 4-5am and then start getting ready to rush dive from around 7-8am. It's pretty exhausting and demanding so it's not recommended for the average holiday-cum-work diver.
Pulau Tioman runs tend to leave Singapore around the same time, with the same 4hr Mini-van rides, but you get to overnight on the mainland and take a 1hr speedboat ride out to the island. Accomodation varies between operators from Very Basic to passable (no stars still).
The Best and most comfortable route to the islands by FAR is as recommended by Live_in_Sin earlier and that is to go to the Dayang/Aur Islands via Live-On-Boards. They aren't MUCH more expensive, give and take USD50-75 difference, but far more leisurely and comfortable. You'll only need to clear immigration once, (which is tiring and horrendous, if you go by land, SERIOUSLY!) and you can have undisturbed sleep in your bed all the way till the Dawn dive.
The MV Whitemanta and MV Blackmanta (more expensive) are pretty much the best LOBS operating from Singapore (I have absolutely no affiliations with them) and are hard to beat even compared to the Boats around the region, so you can't go wrong. I've personally only dove once with them and done the land route 3 times (always swearing off it forever after each trip), and now, I can only imagine going to those islands that way.
Great BBQs too. Good Luck Bob!