Why were Taxila and Ujjayini strategically important for the Mauryan Empire?

They were located along important trade routes.

The correct answer is Option 2 - They were located along important trade routes.

There were five major political centres in the Mauryan empire – the capital Pataliputra and the provincial centres of Taxila, Ujjayini, Tosali and Suvarnagiri, all mentioned in Asokan inscriptions. If we examine the content of these inscriptions, we find virtually the same message engraved everywhere – from the present-day North West Frontier Provinces of Pakistan, to Andhra Pradesh, Orissa and Uttarakhand in India. Could this vast empire have had a uniform administrative system? Historians have increasingly come to realise that this is unlikely. The regions included within the empire were just too diverse. Imagine the contrast between the hilly terrain of Afghanistan and the coast of Orissa. It is likely that administrative control was strongest in areas around the capital and the provincial centres. These centres were carefully chosen, both Taxila and Ujjayini being situated on important long-distance trade routes, while Suvarnagiri (literally, the golden mountain) was possibly important for tapping the gold mines of Karnataka.