Is there good mobile phone coverage in Queenstown?

Telstra and Optus have great coverage

We are with Telstra for phone & Dodo for internet ...no problems.

Yes, we find Telstra the best coverage and have had no real problem with it.

We drove through Queenstown last month on our annual holiday to Tas and found that my Telstra mobile and my wife's Optus one worked well in town, I had coverage from Rosebery right through to Derwent Bridge apart from a couple of spots near Mt Arrowsmith where the wife's Optus service worked better

Coverage by Telstra and other service providers using the Telstra network is excellent. Optus and Vodafone have limited or no coverage in the district.