Site visited just recently (July 2013). Mtskheta lies just outside Tbilisi city limits and is easily accessible by local marszrutka (from Didube bus station, quite frequent buses, approximately every 20-30 minutes, the whole journey takes similar time, ticket costs 1 Lari per person).
Mtskheta as a town (not more than 5 thousand inhabitants) is a small relaxing place, very quiet comparing to busy (and hot) Tbilisi, there are some private flats for rent (rooms) - full list of them available from local tourist information (just outside Svetitskhoveli Cathedral).
It is possible to visit all 3 places (Svetitskhoveli Cathedral, Jvari and Samtawro monasteries) in one day but at least visit to Jvari requires some preparation. It can be reached by foot (ask for details at tourist info spot) or by taxi (count at least 20 Lari for both ways). All 3 places may as far be visited free of charge.