Mt Parnitha, about 25km north of Athens, comprises a number of smaller peaks, the highest of which is Karavola (1413m), tall enough to get snow in winter. The forest was badly burned in 2007 but has rebounded well. There are many caves and much wildlife, including red deer. The park is criss-crossed by hiking trails, with two large, full-featured hiking lodges. It's popular for mountain biking as well.
The easiest way to explore is on the path (about a 45-minute walk) through Tatoi, the 4000-hectare grounds of the former summer palace (closed); follow Tatoi Rd out of Varibobi and look for a small trail sign on the right. For other common trails, see Activities on the park website, or contact EOS in Athens for more current advice (the site is not well maintained).