Shrewsbury is a major rail hub, and sits on a number of busy lines, including Birmingham to Aberystwyth, London to Wrexham and Cardiff to Holyhead. It's not much more than an hour from Birmingham, Cardiff or Manchester, so it's easily visited if you are staying at one of these bigger cities.
Check your ticket prices. Because of its location on the Welsh border, it can be cheaper to break your journey in Shrewsbury, than to buy a direct ticket from England to Wales.
Shrewsbury has a very good train service, both concerning "normal" trains like the Newport - Birmingham line and also the special train of the Heart of Wales Line. This train starts in Swansea, follows a route through the beautiful scenery of South Wales and ends in Shrewsbury. Of course, you can also go the other way, from Shrewsbury to Swansea.
For transportation within Shrewsbury:Walk! The old town is not big, many streets are narrow, there is a large pedestrian precinct and I got the feeling that you're faster walking than driving a car.
Just a mention that the Train Station is about as centrally located as a station can be in a medieval town, and the bus station is quite close to that. So don't worry about pricey taxi transfers from the station to the centre.