Quick answer: The best time to visit Prague is April–May or September–October. Expect a mid-range budget of about €70 per day. Visa: Schengen area — 90/180 rule applies for non-EU passports.
Why this window
Prague before 8am belongs to you; after 10am to the crowds. This plan flips the classic sights to early mornings and fills afternoons with neighborhoods tourists skip.