Although climbing Snowdon is clearly beyond the scope of this guide, the old Miners' Track allows a taste of real hill walking, without all that strenuous up and down business.
As the little car park at the top of the Llanberis Pass seems to be permanently full, it is best to park in the Nant Peris Picnic Area car park, and catch the bus to the Pen-y-Pass Youth Hostel. It's fun too.
From there, follow the Miners' Track sign into the hills. The track is pretty level until shortly after the first of the old mine buildings on the far side of Llyn Llydaw. From here it starts to rise steadily, but does not get really steep until it has rounded Glaslyn.
Note: Despite the relatively easy-going, normal hill-walking precautions (map, compass, whistle, sensible footwear, etc.) should be taken.