I took a taxi from the guesthouse in Dilijan (Nune at the guesthouse called one for me) to Haghartsin and Goshavank. The whole trip took a bit more than three hours and then I went home to the taxi driver and met his lovely family, had coffee, ice cream and chocolate. The Armenian hospitality is great! The taxi tour was 5500 drams (July 2006).
In the evening I met a Dutch couple at the guesthouse who planed to take a taxi to Haghartsin, but walk back. They had bought a book in Yerevan with maps of different walking tours in Armenia, and Haghartsin - Dilijan was one. This sounds like a great option. You can also take a public transport and be dropped on the main road, by the road to Haghartsin, and have a lovely walk along the narrow road, through forests, to Haghartsin Monastery.
Haghartsin Local Customs
In the trees and bushes around Armenian monasteries there are a lot of stripes of cloths tied to the branches. It is a religious custom saying that prayers will be answered if you tie a strip of cloth to a tree near the monastery.
The first picture is from the khachkars standing along the way above Haghartsin and the second picture is taken just by the monastery complex.