If you are going shopping, visiting the theatre or visiting places of historical interest in Stratford, you will be pleased to find that there are lots of car parks as street parking is limited (but you might be lucky). My instructions assume that you will approach Stratford on the A3400 from the South
This site recommends parking at Bridgefoot for visits to the theatre but if you are going to be staying a longish time, I find the Recreation Ground car park a better option as you don't have to go over the bridge into Stratford at all and negotiate the one way system, but turn left into this car park (big sign) just before the bridge and just after the Swan's Nest pub on the left. Then you can walk over the footbridge to the centre of Stratford. The Bridgefoot car park (you follow the one way system round to the right after the bridge) is free for the first hour which may be all that you need to pop into the tourist office and do a little shopping in Bridge Street. The Bridgefoot car park machines give change.
Watch out if you park in Bridge Street itself as there is a half hour limit on parking here (useful if you just want to pop quickly into Boots or M and S) and regular patrols by traffic wardens. Have 50p ready for the machine.
Note that the Recreation Ground only takes money, not cards, and only about 6 of the machines will accept notes and they do not give change!
If you are planning to spend a full day in Stratford, then head for the Windsor Street car park as it is the cheapest option if you are going to be less than four hours. All day parking at the Marina by the river is £4 (prices current December 2015) for the whole day and it is £3 for 4 hours whereas most of the other car parks are at least £1/hour of stay up to four hours so four hours at the recreation ground will cost you £4. Note that Rother Street multistorey is much more expensive - £3 for the first hour, then £2 every hourly increment so one to be avoided!
Windsor Street car park is very central - Head straight over the bridge, right hand lane at the lights and then keep left for the Birmingham Road. Turn left at the first roundabout and the car park is a few yards past the top of Henley Street (a pedestrianised street where The Birthplace is) and right into a multistorey car park - the Windsor Street car park. There are public loos here too but they sometimes leave much to be desired.
Disabled parking There is a small car park, specifically for those with disabled car badges, off the Birmingham Road, plus, of course, spaces reserved for disabled people in all the other car parks.
This map shows you where all these car parks are.