For discovering Amsterdam by public transport and museum visits, March, April, May, September and October are usually the most pleasant months. The weather is often mild enough in that period to spend time outside between stops, while the city stays lively without feeling at its busiest straight away. That makes it easier to travel between museums by tram, metro or bus and still have time for a terrace or a short walk.
In spring, you also often get fresh, clear days that suit a city break well. In autumn, the city settles back into rhythm, with enough daylight for a full day out. Outside these months, it can still work well, but the experience does change. In summer, the crowds call for more patience and planning. In winter, the visit is more about staying indoors and switching smartly between public transport stops, museums and places to eat.