Hogue Riesling is a crowd-pleaser and is about $10 -- cheaper by the case. Widely available. Same for Chateau St. Michelle, but I like Hogue a little better. Both also make a good Gewurtztraminer in the same price range if you want a little variety. These are fruity, refreshing, and not particularly high alcohol so nobody's going to get bombed.
On the red side, PP's Rioja suggestion is yummy, but reliable Rioja (LAN and Marques de Caceras are both widely available) starts at about 14 or 15 and goes up. If you want to stay around $10 or under, you can do anything from Cline, or Blackstone, or Big House Red (the budget label of Bonny Doon), or Red Truck (the budget label of Cline). Or find a Chilean Merlot, or an Argentinian Malbec.
Don't feel like you need to buy Cabernet. Everyone's impressed by that word, but almost all $10 Cabernet sucks. Good Pinot Noir is also hard to find in that price range.