I've just moved house within Shrewsbury (early Dec 2009) and one of the things I wanted was easy walking access to the town centre. I found that the
Globrix website was a useful starting point.
Woodfield Road and surrounding streets in Copthorne/Porthill might be a good idea - interwar semis and detached houses with gardens, 5-10mins walk to the Quarry over the footbridge, 20 mins or so walk into town, roads pretty quiet, frequent buses into town.
Mountfields (bend in the river near Frankwell - Mount Street, Hunter Street etc) is mostly late Victorian, with a range of terraces, semis and a few detached, many with gardens. Very quick to walk into town and not far from the Quarry. There is also a lot of greenery on the doorstep (the photos of the
Severn Way might be useful).
Copthorne Park (Richmond Drive, Westwood Drive, etc) is a bit further out from town - it takes me 30mins to get up there and I like to think that I am reasonably fit. There are frequent buses though. The houses are newer (from the 1950s I think) and mostly have good gardens. There is a park nearby and walks along the river are not far.
Cherry Orchard (Holywell Street, Cleveland Street, etc) is east of the town centre but easily walkable via the footbridge near the Weir. Houses are mostly late Victorian / Edwardian and many have gardens. Some of the surrounding areas are a bit scruffy. Possibly (and this will no doubt annoy lots of people) it's more of a budget option than the ideal choice.
Belle Vue (along and east and west of Belle Vue Road) can be a bit of a trek. Estate agents like to label any house for sale in the south of Shrewsbury as being in Belle Vue, so some of them are a long way out. The area developed piecemeal, mostly in the late 19th century, so there is a wide variety of housing types and sizes of gardens. Personally I'm put off by the railway lines, but there are some really nice properties in the area.