I like how the SE version of the 2012 and up Yaris drives, but earlier ones not so much. This and most other similarly sized cars tend to be noisy on the highway, and cross-winds can blow them around.
But I'm sure it's still possible to drive long distances in them. I recently drove from Detroit to DC and back with my three kids in a Nissan Versa. It was noisy and a strong cross-wind kept pushing it sideways--but I also didn't have any trouble staying awake.
The cargo capacity and handling champion in this segment is the Honda Fit. But you'll have more trouble finding a Fit without a ton of miles in your price range.
Another option from left field is the Suzuki SX4. Suzuki no longer sells cars in the US, but the SX4 offers AWD and has been very reliable in our survey. And, as luck would have it, I found one for sale in your area. Like any used car with more than a few miles, I would have it checked out by a mechanic before buying.