There is a Hotel Mercure in the airport -- you do not need to go outside. In fact, I believe you must go to the hotel before you even reach the immigration officers. If you need to, you can call them at: +31-(0)20-6041339. The airport also has trains beneath the ground level and a train ticket counter in the main entrance hall. Trains between Schiphol and Amsterdam central station run about every 10-15 minutes during the day. The train ride to the city is about the same length of time.

From the central station in Amsterdam, you have directly before the door, a tram and bus station. If you plan destinations, you can go to the GVB (public transport office) in the station (tram/bus station), buy a ticket and ask for route information.

For return to the airport, one of the latest trains leaves central station at 00:43 (12:43 am). The next train is at 01:54. Between 11-12 at night, there are four trains. If you plan accordingly, getting back to the airport should be no problem.