I wouldn't necessarily endorse Park City, but the SLC area (Snowbird, Brighton, Solitude) are your best shot. Utah has always done me just fine in April, much better than Tahoe. It might not be the "Greatest Snow on Earth" come April, but it is still pretty friggin tasty. The lake fuels frequent snows. Considering your narrow travel window, the access to the SLC airport is less than a 40 minute drive. Squaw is a bit more from RNO, but not too much.
Traveling the States and Taking Pictures