As long as you are an experienced rider, riding your motorcycle onto Manhattan will not be a problem; no worse the riding a motorcycle in heavy traffic anywhere else in the country. One traffic law ideocyncracy to be aware of: Within New York City Limits, Right Turn on Red Light is illegal. Outsiders get caught on this all the time. . .
Anyway, there are a fair number of hotels in and near NYC do have parking, either at an attached garage, or they have a relationship with a garage nearby where you can reserve parking along with your hotel room at a reduced rate. Make sure you mention that you are parking motorcycles when you make the reservations. Most garages accept motorcycles, but some do not.
I would strongly suggest getting a hotel that offers parking; it will be more convenient and you will probably save money over what you'll pay at a garage on your own. Don't even think of trying to park on the street.
Be prepared for a fair amount of sticker shock when you reserve a hotel room. Due to the weak dollar, we are awash with European tourists right now here in NYC, and they are bidding up the price of all the hotel rooms. If you're on a budget, you might want to look into a hotel just across the river in NJ. There are a number of hotels just outside the Lincoln tunnel that offer quick cheap or free shuttle bus service into Manhattan, and the cost savings can be considerable.
As for getting around inside NYC, far and away the best way to do it is to bring a good pair of sneakers, and walk everywhere you can. That's what us locals do. When you need to go longer distances, Subway is the way to go. The Subway system can be a bit daunting at first for outsiders. More people ride trains every day in greater NYC on a daily basis, than do in the rest of the country combined. It's the largest commuter rail system on the continent, and the maps and signs aren't always intuitive. But it's cheap -- $7 for an unlimited ride, all day pass. During the day when traffic is heavy, it's faster than cabs, which are also expensive. And contrary to what you see in the movies, you will not end up getting mugged in some remote, seedy industrial area if you get off at the wrong subway stop. You'll just have to ask the station attendant for new directions, and you'll be on your way again. One thing to watch out for on the Subway and in crowded tourist areas in general is pickpockets, though. Violent crime is generally not a problem in NYC anywhere you're likely to go as a tourist. But there are definitely some guys with very quick fingers around here. . .
If you've never been the the city at all before, there are several tourist bus services, such as the Grey Line, that offer all-day, hop-on, hop-off tour buses that go all over NYC. I think these are worthwhile to do on your first day, when you're getting your bearings and trying to get an idea of what's where. You'll see a lot of the city, a lot faster and cheaper than you could do on your own.
One bit etiquitte advice: When you do get turned around and a bit lost, pull off to the side out of the main flow of foot traffic, pull out your map, and get your bearings. Everyone gets lost here, even locals. No problem. Most New Yorkers are even happy to point you in the right direction if you ask. What pisses us off is when the tourists stop smack in the middle of a crowded sidewalk, and block everyone else's right of way while they look at their map, or ogle the tall buildings. It's the NYC equivalent of driving 40mph in the passing lane on the Interstate. Very uncool.
See Central Park. Go up the Empire State Building; it's like $20 or somethign just for the elevator ride, but it's the best view in NYC. Eat Junior's Cheesecake. Make sure to make a couple of trips outside of Midtown, which is where some tourists spend their whole trip. Harlem is very cool (Amateur Night at the Apollo is a trip!). So is downtown Brooklyn. Best way to see the Statue of Liberty is to take the Staten Island Ferry -- it's free (though you wont' get to actually set foot on Liberty Island). See a cheesy Broadway show -- you can get tickets for cheap day of show at the TKTS booth in Times Square, as long as you're not too picky about what you want to see.
Have fun.
