Melville Gate Road is the most sensible route between the A772/Dobbie's cycle paths and the Sheriffhall-Dalkeith cycle path, but lacks cycling infrastructure. It is wide enough to have a segregated cycle route, or at least a shared use pavement.
Nearby, there are a couple of blind junctions, which are dangerous for cyclists. One is for northbound cyclists on Old Dalkeith Road, trying to cross Lugton Brae; it is impossible to see if traffic is approaching on Lugton Brae. The other is for cyclists turning going from the King's Gate to Melville Gate Road. It is difficult to see in both directions.
The Lugton Brae junction would be greatly improved by placing a convex mirror on the wall on the north side of Lugton Brae, so that pedestrians and cyclists can check if traffic is approaching on Lugton Brae.
The King's Gate junction would also benefit from mirrors placed in the right locations, but really needs a controlled crossing.
Alternatively, a shared use pavement/segregated cycle path on the southern side of Old Dalkeith Road would solve a lot of these problems too.