You don't figure out where to go for the first week in April in the last week of August -- you figure it out in early or mid March. Start looking in earnest four or five weeks before, so you can lock down a plan with airfare before the 14 or 21 day window.
Case in point: In late February 2006, it looked like Tahoe had a bust of a season. Then it started snowing on February 27 and stopped six weeks and 450 inches later. Here are my sons (five years old at the time) on the back side of Alpine Meadows on April 9, 2006:

Criteria should include:
- Snowpack in March
- Historical closing date (probably not much of an issue, since most places you'd think about going won't close until mid to late April regardless)
- Availability of lift, lodging, and airfare deals (at least the first two will be plentiful, since most civilians don't consider April "ski season")
Random thoughts... Many Tahoe resorts have a "spring pass" deal in the $150 range, but I'm not sure how prevalent those are elsewhere. The only times I've skied Mammoth have been July 4th weekends; it should be fully open then and has plenty of terrain to keep you interested all week. Snowbird should have good snowpack and deals as well (I stayed slopeside for $100/night, including lift ticket and breakfast, in spring 2008).
Edited by TheDad - 8/24/09 at 6:38pm