Have you tried the walk along the River Mersey - there's flood defences, wildlife & the iron frame bridge named after Henry Simon, one of Manchester's industrialists, and there's what remains of Withington Hospital, which used to be a workhouse - possibilities of urban architecture?
There's also the Fletcher Moss gardens with their glasshouses and displays.
(My grandfather worked for Henry Simon and travelled widely measuring up buildings into which the company's mills could be installed.)
why not take a trip to Dunham Massey,you can visit the home plus it's a deer park.because it's always open to the public and often quite busy the deer are use to people and even at this time of year you can get close.
if you want to go a bit further north then Pennington Flash near Leigh is a brilliant place for bird and water shots - you will also be quite close to the Bridgewater Canal which can be accessed at Astley or Worsley - there are some beautiful b&w houses in Worsley village
Agree with the Pennington Flash recommendation. Another excellent alternative is the area of Rivington on the edge of the West Pennine Moors. It was the home of Lord Leverhulme and he spent a huge amount of money and time laying out ornate terraced gardens, towers and ponds. It's now being reclaimed by nature and is a very popular local spot.
A short drive away there's Jodrell Bank. There's the Indian community along Oxford Road. There's the obvious one of the Library (at least I think that it's the Library - the round building in the centre). IIRC West Didsbury itself has an interesting church. Lots of interesting architecture in and around Oxford Road and parts of the centre. The various University buildings again around Oxford Road.
Also a bit further there's Lyme Park and the Peak District. There's the ship canal.
Further still Liverpool (only 30 minutes or so) has loads and loads of opportunities but Manchester should keep you busy for quite a while.