Amstelveen is best reached from central Amsterdam by tram 25 or metro 51, both of which run from Amsterdam Centraal and reach the Stadshart in about 30 minutes. Schiphol Airport is only 7 km away and connected by direct bus (line 300, every few minutes).
Cycling from central Amsterdam through the Amsterdamse Bos takes around 30 minutes and is by far the most pleasant approach. Most hotels in Amstelveen are close to good transport links.