Air Greenland offers flights from Copenhagen to various airports in Greenland for only EUR 537, currently there is even availability for the (early) summer at entry-level prices. Some connections require you to stay in Kangerlussuaq overnight.
To Copenhagen, you can always get cheap, for example from Hamburg by train or from Berlin with easyJet.
Book nonstop flights to Kangerlussuaq here
Book flights to Nuuk in June here
Book flights to Sisimiut in May here
Book flights to Ilulissat in April here
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