The other option is to approach from the lakeside. Follow the path along the shores of Derwentwater as if headed towards Friar's Crag, and turn inland along the footpath that will take you through Cockshot Wood.
You will come to Borrowdale Road, cross this road and look for the gap on the other side of the road where you can head into the woodland around Castlehead. The hillside is too steep to climb on this side, but just follow the circular footpath round until you see the path headed to the top.
Once you are at the top, you are rewarded with one of the best views of Derwentwater you could imagine. I've been up there on numerous occasions and this is a popular spot for professional and amateur photographers, so why not head up and grab yourself a view that you will have no doubt seen on countless websites and calendars!
You should be able to do the circuit starting from Moot Hall, along the lakeside, up Castlehead and back into Keswick along Springs Road, in a leisurely 60-90 minutes, although be careful as the path around Castlehead can get muddy and slippery after wet or Wintery weather.