Plan far ahead to really save, particularly in the off season. Hotels -- even pretty nice ones -- offer slashed rates throughout the year. Sometimes these rates are published, sometimes not. If you've got a place to stay in mind, call and see what they can offer you. Mention it's your honeymoon, and chances are you'll get a few perks thrown in, like champagne or a room upgrade. If you don't have a hotel preference, spend some time researching your options and making calls. Keep in mind that New York's boroughs can differ dramatically in terms of price; sophisticated Manhattan will always be the most expensive, for example. You may be able to score a deal if you're willing to stay in nearby trendy Brooklyn.
It's a myth that big fun in New York always costs big bucks. Your best bet is Central Park -- it's free, has tons of things to do and is big enough to keep you entertained for a long while. Check out the Central Park website for listings of tours, events and activities (all free or pretty cheap). Or pull out a map and start walking. New York is chock full of street fairs, bazaars and has no shortage of things to see. Take a walking tour of some of the city's most famous neighborhoods, such as TriBeCa, SoHo, Little Italy and Chinatown. Don't forget to check out the museums, wander around Times Square or window shop down Fifth Avenue.
Don't waste money on expensive dinners out, where you'll be competing with other couples for a table and the waiter's attention. Instead, go where the locals go. A trip to New York is not complete without lunch from a hot dog stand or an out-of-the-way deli. Ask your hotel's front desk staff where they go to lunch or dinner (chances are, their suggestions won't break the bank). Better yet, head over to a market and buy dinner materials-- wine, food, tablecloth, cups, utensils, etc. -- and have lunch or an early picnic dinner in Central Park. For a romantic touch, pick up some candles, find a nice quiet spot and enjoy a cozy meal together.
Visitors on a budget should steer clear of the New York's ubiquitous yellow cabs, which are outrageously expensive and will quickly make a big dent in a budget. Instead, haul out a subway map and get to know the vast underground transit system. It's relatively cheap (see if you can buy a weekly pass) and connects virtually every part of the city. Alternatively, try the city's bus system. However, traffic in New York can often be heavy and slow, so walking may be your best bet for many destinations.
Even if you don't have a lot to spend, that's no reason to sit in your hotel every night. Despite its reputation for sky-high prices, New York does have plenty of reasonably-priced nightspots. Check out Chetty Red comedy club in Manhattan, with two-for-one drink specials, or Detour, a jazz club with a $3 happy hour from 4 to 7 p.m. On Wednesday nights, catch a cult/foreign/classic film at Rififi for just $6 as of November 2010. Again, seek out local advice for inexpensive ways to have fun in the evenings.