THERE ARE MANY ways to enjoy New York, but the core of a Big Apple vacation is a good hotel -- and New York City will add 3,389 hotel rooms to the 100,000 existing rooms between now and 1985.

With the price of accommodations in major U.S. cities continuing to rise, New York rates are naturally high on the list. But vacation costs can be shaved with a little advance planning. Bargain-hunting travelers can buy a weekend or other hotel package, pick a small hotel with lower charges (size alone is no guarantee, and location may be a major factor), or stay at a Bed and Breakfast.

Despite this country's serious economic problems, New York's hotel occupancy rate last year was 70 percent, and above the national average, according to Charles Gillett, president of the New York Convention & Visitors Bureau. Convention business, booked far in advance, held up well. Still, no hotel can afford to be complacent in the face of increased operating expenses and added capacity.

For that reasons, and since business travel has dropped somewhat (and business men and women generally don't schedule weekend trips), hotels have a dollars-and-cents incentive to offer Friday-through-Sunday deals to tourists in hopes of filling rooms that otherwise might go empty.

Advance reservations are essential for packages, which can be booked directly with a hotel or through a travel agent. Packages set up by professional tour operators must be booked by an agent. As usual, all descriptive literature should be read carefully. Package content will vary--included may be one or more nights, single or double; one or more meals (remember that a continental breakfast means only juice, rolls and coffee); tickets for sightseeing and the theater, and perhaps complimentary champagne. Check to see if taxes and gratuities are included: the New York State 8 1/4 percent tax and $2 per room per day city occupancy tax, not to mention those 15-20 percent restaurant tips, can take an unexpected bite out of your budget.

Some packages are restricted to certain arrival days or periods. Most represent a savings over the regular "rack" rate--the standard room rate quoted by a hotel in its brochures and often to guests who walk in off the street and fail to ask if any special deals are available. But sometimes the actual savings, upon closer inspection and price comparison (where possible) of the individual items in the package, may amount to only a few dollars.

In certain cases, however, such an effort to figure savings may prove misleading because a hotel (depending on how heavily it is booked) may be able to give a guest one of its top-priced rooms, which automatically makes the package a big bargain.

More than 200 packages are listed in the Winter 1982-83 "New York City Tour Package Directory" published by the Convention & Visitors Bureau. The prices can be compared with rack rates listed in the brochure, "Hotels in New York City," a handy miniguide also published by the Bureau. Unfortunately, in both cases, some prices have recently been raised and some packages have been changed. A revised spring/summer edition is expected to be available by the end of next month, according to a Bureau spokesman, but the current edition remains a useful reference. Below are a few examples of what's available:

Helmsley Palace, 455 Madison Ave., promises a "Royal Weekend" in one of its two packages--two nights (Friday arrival) featuring deluxe accommodations for two, Saturday brunch for two, and Sunday continental breakfast for two. Cost: $240 (new rack rates run from $180 to $225 per night, double).

Milford Plaza, 270 West 45th St., features four packages. One, "New York Lights," offers two nights (arrival any day, taxes included); choice of admission to the Empire State Building, United Nations, Lincoln Center, The New York Experience or Backstage on Broadway tour; choice of Circle Line Cruise or Gray Line bus tour No. 1, 2 or 7; choice of helicopter view of New York or Gray Line bus tour No. 3, 4 or 5; and orchestra ticket to Broadway show (guests can specify a choice of three favorites and hotel will try to pick one). Cost: $147 per person double, $200 single (rack rates for a double range from $61 to $81 a night).

New York Sheraton, Seventh Avenue at 56th Street, lists six packages. Its "New York Sheraton Holiday" offers 3 three or 4 four nights; continental breakfast each morning; orchestra ticket to Broadway show; admission to New York Experience; two-hour bus tour (or optional helicopter tour--$4 additional per person); visit to Empire State Building; and entertainment, dancing, one cocktail at Sally's. Cost (3 (three nights): $173 per person double, $ $275 single (rack rates for a double range from $95 to $125 a night).

Bed & and Breakfasts, which are not listed in the directory, are a grass-roots response to the cost of hotel-motel tourist accommodations. Usually the B&B experience involves sharing someone's home or apartment. While even B&B prices have risen, they are generally well below hotel rates and offer a more personal approach to travel.

Urban Ventures Inc., one of the agencies handling reservations for B&Bs located primarily in Manhattan, represents more than 300 accommodations including 60 apartments without hosts. They range from a spare room to Fifth Avenue suites, with prices from $25 a night single to $75 double. For a B&B brochure, and information on special tour packages, write Urban Ventures, Box 426, New York 10024 (212-662-1234).

None of the directory packages include transportation to New York. Such all-inclusive packages can be purchased from travel agents and transportation companies.