The most convenient anchorage is off the floating dock below the Grenfell Hospital. Unfortunately this is in the turning circle for any large vessel using the harbour and you will be asked to move when ship is due. Anchoring 300-400m further north (towards the head of the harbour) keeps the vessel clear of shipping movements, but means a longer row ashore.
By far the best place to land a dinghy is at the floating dock opposite the Grenfell Hospital. Use the north side of the dock as a whale watching boat boards passengers on the south side. Water is available by jerry can from the Grenfell Centre. It is about a 20 minute walk from the floating dock to the shopping centre where there is a supermarket, liquor store, clothing stores, service station, laundry, autoparts store that will order in anything they do not have in stock, etc. Most things and services are available in St Anthony, but may not be immediately obvious. Ask the locals, who are friendly and helpful.