Ways of getting to Stratford-upon-Avon - trains, buses, by car and simply walking there.
The town has rail links which offer trains from Birmingham (Snow Hill station) - there are several services per hour and these ake around 45 minutes.

From London (Marylebone or Euston) - most services involve going to Birmingham and changing trains with the journey taking around 2-3/4 hours - there are a couple of trains a day from London Marylebone which go directly and take about 2 hours.
Stratford-upon-Avon railway station is to the north of the town and so involves a little bit of a walk into the centre - there are plenty of local buses available as well though. There are several Express Buses serving the town - for instance you can get a daily coach to the town from Oxford in around an hour, two a day from London Victoria which take a little over 3 hours and one a day from Birmingham which takes an hour.
In truth probably most visitors will get too and from the town by car - there are plenty of car
parks available several just a few minutes walk from the centre (for instance on Bridgeway) and plenty more availability can be found on the other side of the River Avon. Car parking charges in the central carparks are currently (August 2014) UKstg1 per hour and are Pay and Display. Main roads into the town include the A439 which takes you north to the A46 and then connects with the M40 at Junction 15 (easily the quickest although not the shortest in mileage if heading towards Banbury, Oxford and London) and the A46 (heading
West) which goes to Worcester.
Cycling around particularly the Old Town is pretty easy although there really is a lot traffic around the oneway system near the car parks on weekends - the other way to get into town is to walk in along the beautiful Stratford-upon-Avon Canal towpath of course.
The town is full of restaurants, cafes, pubs and sadly fast-food outlets - quite often the pubic houses are situated in the old picturesque buildings - particularly around the Old Town area and Church Street. The beautiful River Avon cuts right through the town - there are all sorts of boat trips available and also small boats can be hired for an hour or two.

The photographs shown above and to the right were taken a little way outside of town and show Mary Arden's House, Anne Hathaways Cottage and the beautiful Church of St. Peters at Wooton Wawen.
The locations are possibly a little far to walk too from the centre of town (but done easily enough if cycling) - perhaps (apart from on a bike) the obvious way to go is to drive to them before or after visiting Stratford-upon-Avon town.
Bear in mind that apart from the church the various "Shakespeare" locations have admission charges - take a look at
shakespeare org which shows the
ticket prices, options and so on.