The Bayreuth Festival runs through July and August and is the obvious draw, but getting tickets is notoriously difficult — the waiting list operates over several years, though last-minute returns and online cancellations do appear. If you're coming for the festival, book accommodation a year or more in advance.
Outside the festival period, Bayreuth is calm, easy to navigate, and considerably cheaper. Spring and early summer are pleasant for the Hermitage gardens. Winter is quiet but atmospheric, and the Margravial Opera House runs its own concert series during the off-season.