Flight
If you are flying into JFK, you'll take a monorail that we call the AirTrain to a station called Jamaica. At that station, you get on the LIRR (Long Island Rail Road) and then go to Grand Central Station or Penn Station, depending on which is closer to your hotel.
Flight
If you are flying into LaGuardia (LGA), take the M60+ Bus or the M70 Bus. Either will take you to a subway that gets you into the city, but I personally find the M60+ a little easier. For the M60+, I would get off at Astoria Blvd. (in Queens) and take the N/W train to Manhattan. You COULD take the M60+ into Manhattan and get out at the 2/3 or 4/5/6 subway in Harlem, BUT those subway stations can be a little hectic. For the M70 Bus, you'll take it to a station called Jackson Heights/Roosevelt Ave. There, you can catch the 7, R, or F train into Manhattan. But just for convenience's sake, I would recommend taking the M60+ if possible.
Train
For just general travel throughout your weekend, walking is the best way to see the city, but the subway is also something to be experienced. So if you do take the subway, again, use the apps for directions and times.
Hotel
A couple of Mariuttos have started booking a place here. It's a fine hotel in a fine part of town and decently priced. However, please find a place that best suits your needs. Downtown, Midtown, and anything south of 90th Street is fine. I would avoid looking for hotels outside of Manhattan.