I went there quite a few years ago now - from Europe rather than from the US, and loved the place.

SFJ (Kangerlussuaq - Søndre Strømfjord in Danish) is quite a hub for GL, and you can easily get flights from there up to Ilulissat, which is a must-see destination, for the icefjord alone. I can't overstate what an amazing sight the icefjord is: it may just rank as the single most impressive natural phenomenon I've ever seen.

Ilulissat is the nearest thing to a big town in this area, and quite a good base to start out from. You can then ferry-hop to nearby Qasigiannguit (good walking, lots of seals, and a beautiful little old harbour), Aasiaat (to view marine life, and wander round the traditional smokehouses dotted around the old part of town), Qeqertarsuaq (aka Disko Island - also good for walking around some bizarre rock formations, plus dog sledding up on the ice pack, even when it's passable down in town).

A longer ferry trip from Ilulissat takes you to Uummannaq, perched on a slope and dominated by a giant, heart-shaped rock. From there, it's a relatively short hop to Qaanaaq (which is New Thule - where the residents from Pituffik were re-sited when the air base was built).

Note that if your flight touches down at Pituffik, you will need a transit permit, as it's technically outside the Kingdom of Denmark.