The best months for Syunik are June through September, when the mountain roads are reliably passable and the days are long enough to cover the distances involved. Summer days on the plateau are warm — often pleasantly so — but nights cool down sharply at altitude, and you will want layers even in July. The gorges around Tatev and Goris hold their warmth better, but the high ground does not.
Spring, from April into May, brings wildflowers to the plateau and the gorge slopes in extraordinary numbers, and the landscape is green in a way it never quite manages later in the year. The downside is mud: dirt tracks and mountain roads can become genuinely impassable after spring rains, and a vehicle that managed a route in autumn may be stopped by the same road in April. The Ughtasar petroglyphs, high on the mountain, are typically inaccessible until June at the earliest.
Autumn — September and October — is often the most pleasant time. The summer crowds (such as they are in Syunik) have thinned, the air is clear, and the colours in the gorges and forests around Tatev are remarkable. The Wings of Tatev cable car and Tatev Monastery are both open and considerably less busy than in high summer.
Winter is harsh. Snow closes many mountain roads from November onward, and the high plateau around Ughtasar is buried until late spring. The cable car to Tatev suspends operation during bad weather and may be closed for days at a time. Goris and Kapan remain accessible year-round, but there is limited reason to come to Syunik in winter unless you are specifically interested in the provincial towns rather than the landscape.