Recommended time to visit Armenia is May-June or late September-October. Both summer and winters are quite harsh and hence not highly recommended for travel.
It is always good to understand the geography of a place before you travel. This helps in planning to see all the monuments in one area to avoid repeated travels. Especially if you want to explore the city by walking.
Convert your currency to US Dollars before travelling as you get better exchange rate in Armenia for Dollars. Within Armenia, they only use Armenian Drams. In any case, even supermarkets offer currency exchange services.
Armenia offers visa on arrival for Indians and this means you just have to pay 7$ for visa at the airport.
Make sure to carry 2-pin adapter for chargers
Mobile service providers are accessible in the airports as you exit and offer good plans. We got the one from Vivacell (MTS) for 2,800 drams with unlimited local calls (important when you have to coordinate for tours etc.)
Metro is accessible and affordable (less than 1$ for one way trip) and runs from 7 am to 11 pm
Safe place to travel with several women visible in public and lesser crime rates.
Vernissage Market is the best place to shop for souvenirs and local art. Make sure to buy anything with pomegranate or Mt. Ararat on it as these are seen as Armenian symbols.
Strongly recommend walking around the city especially in the mornings and late evenings to discover the place and its essence.