A car is essential. Okanogan County is enormous — larger than some US states — and the distances between any two points of interest are significant. The town of Okanogan itself is small enough to walk, but you are not here for the town. Trailheads for the Pasayten Wilderness are an hour or more up forest roads; fruit stands and scenic drives require a vehicle; Omak is a short drive across the river. There is no public transit of any practical value for visitors, and no bike-share infrastructure.
Road conditions matter more here than in most places. Forest Service roads accessing the Pasayten and national forest can require high clearance, and some are impassable after rain. Check current conditions with the Okanogan-Wenatchee National Forest ranger station before heading into the backcountry. In winter, many mountain roads are closed.
Gas up in town before heading out — stations become sparse quickly once you leave the highway corridor.