Variations in Daylight Savings Time do not count. For example, parts of Arizona (Navajo reservation) observe DST but most do not: however, Arizona is not an answer.
Majority is in Pacific time zone, but most of Malheur County (around Ontario, OR) observes the Mountain Time Zone.
Alaskan, Hawaiian
Majority is in Alaskan time zone, but most of the Aleutian islands are in Hawaiian/Aleutian time zone
Pacific, Mountain
South is in Mountain time zone, but the northern panhandle is in Pacific time zone
Mountain, Central
Majority is in Central time zone, but southwest area is in Mountain time zone
Mountain, Central
Western part is in Mountain time zone, eastern part is in Central time zone
Pacific, Mountain
Majority is in Pacific time zone, but West Wendover, Nevada is in the Mountain time zone (officially) and Jackpot, Nevada unofficially observes Mountain time.
Mountain, Central
Majority is in Central time zone, but parts of extreme west are in Mountain time zone
Time zones
States
Explanation
Central, Eastern
Majority is in Eastern time zone, but northwest and southwest corners are in Central time zone
Central, Eastern
Western part is in Central time zone, but eastern part is in Eastern time zone
Central, Eastern
Majority is in Eastern time zone, but parts of Panhandle are in Eastern time zone
Mountain, Central
Majority is in Central time zone, but area of extreme west around El Paso is in Mountain time zone
Mountain, Central
Majority is in Central time zone, but western part is in Mountain time zone
Central, Eastern
Majority (western part) is in Central time zone, but eastern part is in Eastern time zone
Central, Eastern
Majority is in Eastern time zone, but counties of Upper Peninsula bordering Wisconsin are in Central time zone