Okay, here is an insider/outsider perspective of NYC.
Europeans generally obey pedestrian/traffic laws. NYC, for the most part just goes with the flow. Hardly any pedestrian stops at a red light unless they are the main traffic north/south arteries that can easily get you killed.
Many Euros also like to give to the poor and NYC, like many big cities, has it's fair share of scams going on at all times. I'm not saying don't give money to anyone but, don't give money to anyone in NYC. If you are a tourist you'll be on a tight budget anyway (I assume).
Midtown and Downtown Manhattan seems very safe, it can get a bit shady when you get closer to the "outsides" of Manhattan but even then I never really felt threatened.
If you stay in the touristy areas you should be completely fine. Manhattan is always well lit and is always busy so there shouldn't really be much of a problem with gangs of rapists and muggers or whatever somebody picked up from a movie.
MSG to me, especially around Penn Station feels very safe, so I'm not sure why people are telling you to "watch your back".
I mean, for the most part "big city rules" should apply which has nothing to do with NYC but more like with the nature of bigger cities.
It should be common sense to not carry around valuables in a backpack in a tight crowd and not pay attention to your backpack or your purse.
I love visiting Manhattan and would have no problem living there if I had the choice, it feels no less safe of more dangerous than downtown Pittsburgh to me.
One thing that's really odd about Manhattan is that you can easily overlook some landmarks if you don't pay attention. I have missed out on taking some kick ass pictures of the Empire State Building even though I stood right in front of it. This town is literally a canyon of skyscrapers and sometimes you are standing in front of a famous landmark without realizing.
As a tourist, take your time and soak it all in. Don't let the busy nature of Manhattan infect you that makes you move along quickly.
That being said, don't stand in the middle of a side walk to take pictures. People will get pissed because you are literally blocking the flow.
If you and your buddies have to take a break to take pictures, look at a map or just for a huddle make sure you move out of the way and stand to the side.
If in doubt, don't hesitate to ask police officers (not the traffic cops) who are sitting in their cars or just patrolling the streets. NYPD has a bad reputation as being tough jackasses, but they were the friendliest bunch I have encountered in my travels. They will ask where you are from if you have an accent and you might even get into a conversation with them which is really cool.
Hope it helps and hope you guys will have a great trip.
My first trip to MSG was like a dream, a blur and it can be a bit overwhelming especially if you only know the Garden from your tv/computer screen. Take it all in!
P.S.: I should prob mention some of the negatives too so you won't be disappointed.
Manhattan REALLY stinks in the summer time. I've been told it's because of rotting critter carcasses and the sewers and, well because it's a damn big city.
Winter is bearable but in the summer time you will encounter a VERY foul odor.
I've been to London, LA, Berlin, Cologne and other huge city, NYC is the worst smell offender. It get's much better once you get to downtown WTC/Battery Park. But Midtown stinks.
Also, the heat up until September even October is something to behold. The layout of the city makes it very hard for heat to escape from groundlevel and you will be pretty toasty. So make sure you dress right or have at least a fresh t-shirt you can change into.
I walked from 51st to MSG in a very slow pace in to watch a game in November and walking doesn't make me sweat at all but by the time I arrived at the Garden I was drenched.
