For a cut above the most inexpensive tires, I've had success with:

Michelin World Tours, $12.99 each at this site.

or

Panaracer Paselas, at $14.99 each

or, for slightly better flat protection,

Panaracer Paselas with Tourguard, for $17.99.

It's likely you can find some of these tires cheaper at other retailers, but this gives you a few options.