There is a thread in the Mileage Run subforum that is titled something like "Cheap Economy Fares." Mostly domestic but occasionally interesting and, as noted above, many are intra Europe so you can always get across the pond for cheap and make a go of it from there. A couple examples of recent deals had:

My parents are flying in a few weeks MIA-FCO R/T N/S on ITA for around $700 all-in, and that includes seat assignment. The sale was around Thanksgiving (courtesy of an ITA promo email).

I took a family of five N/S BOS-DUB in PS on DL for about $800 over Christmas and New Year's, and had flights to/from DUB and the continent for around $50 each in RyanAir. I picked cities with multiple flights a day and the costs included carryon and seat assignments. Booked close in (sub-30 days) and we were flexible on where to go. And to your wife's interests, we stayed on a house boat in Amsterdam for New Year's.

All it took was some patience and gaming. I recommend using Google Flights like many others here do for an initial search (eg, Miami to Europe) on specific dates that will give you a map with a range of minimum prices to different cities, and then you may experiment from there. Not for everyone but to me planning is part of the adventure...