Blackberry is the closest to North Conway and right in front of Sundown ledge.
Actually Covered Bridge is the closest to N. Conway, you can walk to Sundown from the sites, and there is a back way from the CG right down to the Whitehorse / Cathedral area that avoids all the congestion of 302 and the time consuming drive back and forth on the Kanc. Blackberry Crossing is the next closest, being essentially across the Kanc from Covered Bridge, and is best accessed from N. Conway via the same back roads as Covered Brideg. I don't recall the names of the roads, just know them by sight. A quick googlemap search will make it obvious, however.
Covered Bridge is closed for the season. Blackberry is open, at least it was last weekend. They are right across the street from each other, so distance to N. Conway is negligible. However, Covered Bridge is closer to Sundown & Crack in the Woods.
I would say covered bridge, but if that's closed Blackberry would be next. Not sure if the the back road is closed yet, this way you could avoid the round about way to N Conway/ traffic,and get right to Cathedral/Whitehorse. Plus there are some decent crags in the general vicinity.