For the vast majority of tourists, Vagar Island is going to be your gateway to the rest of the beautiful Faroe Islands. Unless you happen to be coming in by ferry or a cruise liner, you'll be flying over and alongside some dramatic coastlines before landing in Vagar Airport, the only actual airport in the country.
The airport itself is, unsurprisingly on the petite side. If you haven't already arranged a car in advance, you'll definitely want to rent one. Getting around the Faroes is best done by car. Sure there is some public transportation, and you definitely should take the ferries between islands or perhaps a helicopter ride (it's way cheaper than you'd expect thanks to Danish subsidies), but the islands are pretty small overall and easy to navigate by car.
Besides the fact that you'll be operating on your own time tables, having a rental car will enable you to see so much more of the islands. There's a number of small villages that depending on your interest, you can cruise into, spend 20-30 mins, and move on to the next. And driving through the one-lane tunnels in some places can add a little extra hint of adventure to an otherwise quite remote, European destination.
One of the first things I did upon arriving in Vagar, besides struggle to learn how to drive stick shift, was to head over to the east side of Leitisvatn, which is the largest lake in the Faroe Islands. There's a nice path that takes you along the lake and all the way out to the ocean. Walking the path provided some refreshingly crisp clean air after making my way to Vagar by way of Copenhagen from the States.
The path itself isn't very challenging, but if you wander off a bit, the climbing and be a bit steep at times. But you kinda want to wander off to get those amazing views. This is a place where every which way you turn your head, it's just sheer delight that you're there. The mountains and cliffs are set against blue lakes and oceans and waterfalls and covered in deep greens dotted with some of the many sheep on the islands.
Speaking of sheep, you'll see a lot of them in the Faroes. Like, a lot a lot. Walking the path, I definitely encountered a few just hanging around. When you get to the end of the path, there is a a waterfall named Bøsdalafossur that flows from the lake 30m down into the ocean.
Vagar Island itself is home to one of the most beautiful waterfalls I've ever seen. Tucked quietly away in the small village of Gásadalur, a small stream turns into the postcard image of the Faroes. There's also some great views of the islet Tindhólmur from the village of Bøur, which you're actually going to drive past on your way to Gásadalur.
Just spouting this information out makes me miss these serene islands so much. They would be an incredible place to catch the northern lights from, if you need another excuse for why you must visit the Faroes.
Even though Vagar Island has its share of Faroese beauty, lodging options, as elsewhere in the Faroes, is a bit limited. I spent a night at Hotel Vagar. Technically you could walk to it from the airport, but you already know that you need a car and it's worth it to save a bit of hassle and to just drive the short distance over there.
I wasn't sure what to expect, but I can say that the internet speeds at Hotel Vagar were much better than I expected. I was able to use Google Hangouts to do some video conferences with colleagues from there, and it worked surprisingly well. There was also curiously enough what looked like a mini-golf literally right outside my hotel room window, the reason for which, I never quite figured out.
If you have any reservations about staying at a hotel airport, I wouldn't worry too much. There's only a handful of daily flights operating on Vagar, and they're all during the day so far as I know. Well, if you visit during midnight sun, it all seems like daytime anyways, so I guess it's hard to say, but I think they were only flying when I was awake. Either way, with landscapes like these, you want to get out and explore!
Once you've explored Vagar Island, you can take a ferry to neighboring Mykines Island to check out the puffins. The island is also connected by subsea tunnel to the neighboring island of Streymoy, home of the Faroese capital of Torshavn. The more you look into the Faroes, the more you'll see there is to discover!