Intermediates and above
Walk the Yr Wyddfa (Snowdon) Range from Pen-y-Pass, the most popular start point to summit Mount Snowdon. From here there are numerous hiking routes, including several which take you to the summit. Perhaps the most popular is the Pyg Track (nothing to do with pigs!) which is a steep but clear route offering views of Mount Snowdon for most of the way (weather permitting!). There is also the more gentle, fully accessible gravel Miners Path which gently circles around to Snowdon's lakes - a great option for those who don't want to summit but wish to soak up the amazing views of Snowdon. Finally, there is the Crib Goch route, starting on the Pyg Track and veering off and steeply up onto what is considered one of the best grade 1 scrambles in the UK - this is for experienced hikers only and can be very dangerous in bad weather.
Note that walking from here is very popular, so avoid obvious times if possible and make use of the park and ride. There are other very enjoyable and less busy routes that are worth considering.
Free public access
A very challanging route with dogs and keep under control around sheep
Cafe at Pen y Pass Centre and at the summit when the train is running
Toilets at Pen y Pass centre and the summit when trains are running
Plenty of options nearby
For more info check out the Eryri National Park Website