I've "been" to several of the Trappist breweries: Westmalle, Rochefort, Orval, Westvleteren, and Achel. I, however, didn't get a tour at all of them so had to make do with a visit to the cafe and perhaps (in the case of Westmalle) a video tour. Of the ones I had an actual tour of, I think Orval may be the most interesting. In addition to the brewery one can tour the ruins of the monastery. Achel, by contrast, is closer to a brewpub with the small, modern brewery behind glass and the cafe service similar to cafeteria style. Achel does/did have a great shop adjacent though where most/all of the other Trappist beers, glasses, etc. could be purchased.
I'll second the recommendation for 3 Fonteinen. Not only do they serve one of my favorite beers, they also have an excellent menu with several authentic regional dishes. They are open for lunch & dinner (closed in between) and I believe they are closed on Tuesdays & Wednesdays.
The Centrum Hotel across the street from 3 Fonteinen has a cafe that served quite a few of the other (Boon & Girardin are what I remember) lambics. I wouldn't recommend staying at the hotel during a honeymoon though; it's good but very bare-bones.
If you like saison, I would recommend a visit to the Dupont brewery tap. No matter how good the Saison Dupont I've had anywhere else, it pales in comparison when consumed across the street from where it's made. They usually have the full product line available given enough time to bring something up from the cellar and chill in the cooler. A modest knowledge of French will come in handy as I don't recall how well the lady that runs the place speaks English.