One canal walk I "discovered" for myself a few years ago took me on a circular walk round the North of the city centre and it takes you in to areas that not many people go in to.
You can easily follow the description of the walk below on Google Maps, selecting Map view.
I started it near Aston University, near Dartmouth Middleway and Dartmouth Circus. There is plenty of parking space on a Sunday in the side streets around Aston University.
The canal that runs alongside Aston University is the Digbeth Branch Canal. I entered the canal somewhere near Lister Street (I cant remember the exact spot) and walked South, crossing through Eastside (near the Thinktank museum). This area in Eastside is due to change a lot in the next year or so and it would be interesting to see it now, then in a couple of years when it has all been developed.
The canal continues south, then "bends" towards the city centre. The canal does go straight on here into Typhoo Wharf (but I believe this is blocked off). Typhoo Wharf has also plans for redevelopment so this area may change a lot in the next few years.
https://bigcityplan.birmingham.gov.uk/digbeth/
But just before Typhoo Wharf you turn left and go onto the Grand Union Canal. This goes South East for a short distance, then at Bordesley Junction (near Glover St) you turn left onto the other "leg" of the Grtand Union Canal that goes North (walking under Glover Street).
You continue North up the Grand Union Canal for a fair distance (walking alongside Heartlands Parkway) until you find yourself under Spaghetti Junction (this is called Salford Junction). Here it meets the Birmingham And Fazeley canal.
The Birmingham and Fazeley Canal goes off to the North East, but you go on to the section of the Birmingham and Fazeley Canal that goes South West, down through Aston.
You continue Southwards down this canal till you get to Dartmouth Circus, but whereas the Birmingham and Fazeley canal goes straight ahead into Birmingham City Centre, you take the left "leg" that goes off South East and you find yourself back on the Digbeth Branch Canal, which is where you started.
Soon you reach the place where you joined the canal and started the walk.
You can do this walk totally on canal footpaths, I know because I have done it.
The description above is an anti clockwise walk, but you can of course do it the other way round, clockwise.
I have to say I have not done this walk for at least 5 years, but I found it a fascinating walk and it gave me a totally different view of Birmingham that you never see by driving around it.
I must admit I feel less safe on some of these deserted canal tow paths than I did a few years ago (particularly with an expensive camera), but if anyone wants to organize this walk I would be happy to join them if there were a group of us.