Streets running East and West that connect with an East and West Avenue should be a __________.

The most suitable term for streets running East and West that connect with an East and West Avenue is "Drive." This designation typically implies a thoroughfare that provides a direct route for traffic and is often associated with residential areas or connections to major roadways.

In urban planning and naming conventions, a "Drive" usually indicates that the street has a certain level of importance in terms of traffic flow and usability, often serving to route vehicles between neighborhoods or major roads efficiently. This fits the context of connecting streets with an avenue, as Avenues often serve as larger, more significant roads.

Other choices do not align with this contextual function as directly. An "Alley" typically refers to a narrow passageway, commonly used for service access rather than major traffic flow. A "Trail" suggests a less formal or unpaved pathway suitable for recreational use, rather than connecting main streets for vehicular traffic. Meanwhile, a "Lane" might refer to a smaller road, but it does not carry the same weight or significance in terms of connectivity as a "Drive," making it a less appropriate choice for this scenario.