If excursions are looked for then Punte del Este is recommended
Although there is a dock the Star Princess to big a ship to berth so a short tender ride is needed.
Puerto Montt is not too attractive but the surrounding area is. There are taxi's available in the harbour area which can be cheaper than an excursion, especially if you are 4 in your party. We did this and went to Lago Llanquihue (largest lake in Chile). Stopped at Puerto Varas (strong German feel to it)and went on to Lago Ensenada. On the way we stopped at the Saltos (Falls) del Rio Petrohue. Very attractive small waterfalls through volcanic rock - however watch out for the midges so take insect repellent!
The town of Frutillar (also on Lago Llanquihue) is meant to be the most German in architecture, etc
There are tours to see battlegrounds (1982 conflict)and wildlife. However most of these by Land Rover or other 4x4's with limited space as there are few roads outside Stanley. There Excursions sold of the ship get booked up quickly.
Many nice English style pubs in Stanley with English beer! The museum is excellent - about 2 miles from tender landing point and there is a free shuttle to and from the museum. Take a taxi to Gypsy Cove ($20 per person) to see the Penguins. Stanley Golf Club is "interesting"
The town itself is just about UK but I would recommend an excursion to nearby lakes, etc. Scenery outside the town just great and there are other attraction such as narrow gauge railway, golf course etc. We went to Bahia Ensenada and saw the end of the Pan American Highway : Alaska 17,848 kilometres away!
If you take an excursion say in the morning you can explore some parts of the own in the afternoon on foot or taxi. The ship berths here so no tenders needed.