A Weekend In Brussels

It's hard to say without knowing what your areas of interest are. Some suggestions might be:

The magnificent Grand Place with its ornate town houses and Town Hall
See the art nouveau town houses in the St Gilles/Ixelles area or around Square Ambiorix.
National Museum of Ancient and Modern Art - huge collection of well known artists with a whole section on Rene Magritte
Musical Instrument Museum - as well as the collection, housed in a magnificent art nouveau former department store
The Cinquantenaire Museums - museums of decorative art, military history, and automobiles housed in a large city park.

Since you're arriving in late April, you may be around for the couple of weeks per year that the Royal Greenhouses at Laeken are opened to the general public.

Negatives - don't bother paying to go inside the Atomium, although it's worth seeing from outside, and don't eat anywhere in rue des Bouchers except Aux Armes de Bruxelles.

Some people here will tell you that there's no point in staying in Brussels and to visit another Belgian city. Ignore them.

I would disagree with Philip. Take at least a day trip in Brugge. It is just one hour from Brussels by train.
My recommendation: On Friday go direct to Brugge, spend Friday night, the whole of Saturday and Saturday night in Brugge, back to Brussels Sunday morning. One day is enough for Brussels.
Amsterdam is a bit far for a day trip.

Sounds like you could use Rick's prioritized summary of main sites in each city at http://www.ricksteves.com/europe/belgium. Click on the city name, and then on "At a Glance." His guidebook has more detail for these sites and others. Monday is the main closure day for museums in Bruges and Brussels, and a few smaller museums in Amsterdam, but neither Saturday nor Sunday should have that problem.

Brussells is adorned with murals on the outsides of many buildings, which range from comical to outright Fine Art. Strolling the city you'll spot many murals, so be sure to look up once in a while.

If you're a beer aficionado (and maybe even if you aren't) try at least 2 or 3 varieties of what is arguably the world's best beer. Same goes for their frites (Belgian fries).

Trying to stay in Brussels for only a day is precisely why people end up disliking the city. There's a lot of really interesting stuff there, but it's quite spread out and you need more than one day to do it justice.

I agree that you should have a look at Rick Steves Snapshot Bruges & Brussels (which now includes Ghent and Antwerp). In it you will find more than enough to keep you busy for 2 days in Belgium, without having to leave the country to see Amsterdam (which not only takes more time, but costs a lot more money than using the local Belgian trains).

You will find that Brussels divides people, and opinions on the other Belgian cities are similarly diverse. I'm not a fan of Brussels at all, but I loved Antwerp, really liked Bruges, and took time to warm to Ghent but liked it in the end. Others have different experiences; hence my advice to learn as much as you can about the options, and see which ones appeal to you.

However, one thing I did love in Brussels was my Art Nouveau Tour with ARAU. If they are giving an English tour when you are in town, take it: http://www.arau.org/en/tours. The Art Nouveau sites are spread out, and the tour takes you into building not open to the public. I feel so strongly positive about it that if I ever go back to Brussels, I will time my visit to coincide with one of their tours.