Iceland served as my first international destination and really opened my eyes to the world and set me on the path I've taken since and visited over 100 countries!
Stark contrast to Greenland which is in fact covered in ice, Iceland has a milder climate especially along its coastline and effectively makes itself a year round destination.
It's also one of the best places in the world to see the Aurora Borealis (Northern Lights), which is truly a marvelous sight to see with your own eyes!
I offer full services for Iceland, especially the western and southern portions. All of the main tourist sights are along the Ring Road, so you will need to rent a car to get to them easily and at your own pace.
Driving in Iceland is not bad, just be sure to get windshield insurance as it is almost certain to prove useful since the roads are made with a mixture that uses volcanic rocks that will chip and easily damage it.
My suggestion is to visit in the winter so that you have a chance to see the auroras, it's not as cold as England or New York would be so you don't need to prepare for an Arctic expedition.
Iceland to me is the perfect country to begin your international travels, as I made this choice for myself at the very beginning.
There are no visa requirements for US citizens visiting for tourism.
No vaccinations are required to enter Iceland.