The Isle of Man is wonderful - it is a bit like stepping back in time. Guide books tend to ignore the island and one of the the best sources of information is here.
You don't say if you are hiring a car. Transport is very good and you can reach most places very easily without hiring a car. There are details of bus and train transport on the website, but it is worth picking up the timetable from the Visitor centre in the Sea Terminal Building when you arrive. The staff are excellent - they are probably the best people to ask about fly fishing .
There is the horse tram along the prom, the steam railway from Douglas to Port Erin, Manx Electric Railway from Douglas to Ramsey and the tram up Snaefell. There is also the Groudle Glen Railway that was built as a Victorian tourist attraction taking visitors to see the polar bears and sea lions kept in an enclosure at the base of the cliffs. The animals are long gone but the railway survives run by enthusiastic volunteers.
There is a lot of history to find too - from the Viking boat burial at Baladoole to the carved crosses found in many of the old churches. The Isle of Man has the oldest parliament in the World and you can visit the site of Tynwald at St Johns. The Manx government still meets here once a year on Tynwald day to read out laws that have been passed.
Visit the Manx Museum in Douglas (free) to find out more. The House of Manannan in Peel also covers the history but is aimed at the short attention, five second soundbite...
There is Peel Castle, Castle Rushen and the ruined Rushen Abbey. Cregneash is a 'folk museum' of old crofts reflecting the way of life 100 years ago. Laxey Wheel is the centre of a major lead mining industry.
You can buy a combined pass covering both transport and the heritage sites.
If you are walkers, there are a lot of easy walks to do and glens to explore. There are wild life boat trips from Port St Mary and Port Erin.