Ah, the age-old question of when to visit the Big Apple without breaking the bank. As a seasoned detective and amateur budget traveler, I can tell you that the answer is simple: Timing is everything.

Let's start by dispelling a myth: New York is never cheap. No matter the season, you will always be paying a premium for the opportunity to experience one of the world's most iconic cities. However, some seasons are less expensive than others, and if you're a smart traveler, you can save a pretty penny by choosing wisely.

The peak tourist season in New York is during the summer months, from June to August. During this time, the weather is warm and the city is bustling with tourists and locals alike. However, this is also the most expensive time to visit, with sky-high hotel prices and long lines at popular attractions.

The winter months, from November to February, are the cheapest time to visit. The weather is chilly, but there are fewer tourists, and many hotels and attractions offer discounts to entice visitors. Just don't forget to pack your warm coat and gloves!

Fall and spring are the "shoulder" seasons in New York, and they offer a happy medium between the high prices of summer and the lower prices of winter. The weather is mild and there are fewer tourists, but you may still face higher prices for hotels and attractions.

Now, if you're looking to save even more money on your trip, there are a few tips and tricks that I've learned over the years. First, be flexible with your travel dates. Weekends and holidays tend to be more expensive, so if you can travel midweek, you may be able to save some cash.

Second, consider staying in a budget-friendly neighborhood, such as the Lower East Side or Washington Heights, instead of the more touristy areas like Times Square. You'll save money on your accommodation and still be close to all the action.

Finally, be mindful of your spending while you're in the city. New York has plenty of free attractions, such as the Central Park Zoo and the High Line, and many museums offer free admission on certain days of the week. Plus, you can save money on food by eating at local delis and food trucks instead of pricey restaurants.

In conclusion, there is no one "cheapest" time to visit New York, but by being flexible and mindful of your spending, you can have an amazing time in the city without breaking the bank. So, go ahead and plan your trip – the city that never sleeps is waiting for you!