Ørestad is a neighborhood in Copenhagen that incorporates the Copenhagen Airport (CPH) and Øresund Line that connects to Malmo, Sweden. Spending only a few nights in Copenhagen, and with an excellent public rail system, I found myself staying at the Crowne Plaza in Ørestad. Nice hotel, but in a super quiet part of town. After six days in arctic Greenland, the hotel was a welcome respite to come back to.
There's really nothing much you're going to want to see in the immediate vicinity aside from maybe the largest shopping center in Denmark, and one of the largest in all of Scandinavia, Field's. Admittedly, I didn't bother to go in. I'm not traveling to shop. Within a few minutes walk, you're at Ørestad station and can hop a train to either the airport or Copenhagen Central Station within 7 minutes. Quick!
View from the Crowne Plaza Copenhagen Towers.