Venice, Italy, is on sale for $856 -- at least that's the round-trip airfare, including taxes and fees, from LAX on Air France. This will sell out quickly, so availability is not guaranteed.
It is for departures Sundays-Wednesdays between April 2 and May 17 and requires a seven-day advance purchase, a Saturday-night stay and no more than a month's stay. You must purchase by March 26.
Info: Air France, (800) 237-2747