Stratford is busiest in summer (July–August), when school holidays bring families and the RSC season is in full swing. The town centre can feel genuinely crowded at these times, and queues at the birthplace and other properties are long. Spring and early autumn are the better times to visit: the gardens are in good form, the crowds are manageable, and the RSC programme is still running.
The RSC season typically runs from spring through early autumn for the main Shakespeare programme, with a reduced winter programme that often includes non-Shakespeare productions. If you are coming primarily for the theatre, check the programme before booking accommodation. The Christmas market in December draws crowds but the town is otherwise quiet in winter, and the indoor sights are accessible throughout the year.
A good outdoor experience requires reasonable weather — the riverside walk, the gardens of New Place, and the cycle to Anne Hathaway's Cottage are all weather-dependent. Stratford's Midlands location means rain is possible at any time.