City and State Sharing a Name: One East, One West

The answer is Albany — but with a clarification:

• Albany, New York — the state capital, located in eastern New York (not "a state west").
• Albany, Oregon — a city in the Willamette Valley, western Oregon.

Other city/state name pairs:

• Kansas City (MO/KS) — straddles two states
• Oklahoma City, OK — city = state name
• Indianapolis, IN — city name contains state name

The "Albany" pair (NY capital + OR city) fits the east/west pattern best.