Would I have time to take a taxi or train to central Amsterdam for a look around and get back with a 4.5 hour layover at Schipol airport.

Probably, if your plane is on time and you get your bags quickly. It's very convenient to catch the train right at the airport, and the ride to Amsterdam Central is about a half hour. However, Schiphol advises being at the airport 3 hours before a departing international flight, so keep that in mind. From our experience, 2 hours prior to departure was sufficient. However, our arriving flight in AMS took so long until it got a gate assignment and we debarked, we decided it wasn't worthwhile rushing into Amsterdam for a half hour visit.

I don't think you'll have time. The check in lines there SUCK, and if you are late, you will really be in trouble. Just hang out at the airport. It's like a big mall.

That seems awful tight- even if your flight lands on time it will most likely take a bit to exit the airport. If you need to be back 2 ahead for the connecting flight, then add ~20 mins each way on the train or taxi into downtown. Well possibly you could have an hour for lunch somewhere, but not much more. Schipol offers many things within the airpot, you might want to check out their website.

I'd advise trying to book an executive lounge so you can relax in comfort while you have a long wait for your ongoing flight.

However, if you find out upon arrival that the flight is delayed you may find you have more time available to explore.

Thanks everyone - I think my parents would freek out if I try to cut it close.