NM 63 runs north from Pecos along the river toward Cowles and the edge of the Pecos Wilderness. The road is a good scenic drive even if you only picnic by the water, but hikers can continue into serious backcountry of spruce, aspen, high meadows and cold trout streams.
The Cowles area is one practical jumping-off point. Conditions change quickly with snow, storms and fire closures, so check with Santa Fe National Forest before planning anything ambitious.