I've fished it several times around the South Accomadation Road bridge before they did the alterations and there are some decent Chub and Roach in there.
Also the Royal Armouries produces some good catches as does the Kirkstall Abbey length
The water quality is a heck of a lot better than it used to be and the fish seem to be thriving. I wouldn't fish it alone though because likewise so does the kn#bhead element.
Around the South Accomadation Road area up to Leeds Bridge is where most of the wino's hang out 
Ohter areas worth a try are the Thwaites Mill length and the Power Station at Stourton. Stu and I put in quite a few days at the power station a few years back and had some cracking fish
Access is pretty limited to most stretches as they haven't been developed as such for fishing. The fishing rights are common ground to the lengths in the town centre and offer free fishing.
Royal Armouries should be the best stretches for ease of access and I will ask the missus when she gets home to make some enquiries as she works for the council (Social services)
Thwaites Mill is day ticket and is easy access from the Mill car park, the Power Station is difficult even for the able bodied