Northern lights

"Where should they go first and where is the best place to see the lights."

Alaska, Yukon, and Northwest Territories. The drier the climate, the better the chance that all the conditions will come together to allow them to view the lights. You can see them in Norway, but the damper weather lowers the chances- you need relatively clear skies and unobstructed horizons.

They will need to be at least as far north as Trondheim, if not farther. The solar storms that cause the northern lights are not predictable more than a few days in advanced. So, if they're dead-set on seeing the lights, they should dedicate at least a week, then plant themselves in that one location and wait. This website from the University of Alaska-Fairbanks provides a short term forecast.

Bill Bryson's "Neither Here Nor There", 1991 starts off in Norway with his hope of seeing the northern lights.

http://www.billbryson.co.uk/index.php/neither-here-nor-there-travels-in-europe/#exract
Chapter 1
In winter Hammerfest is a thirty-hour ride by bus from Oslo, though why anyone would want to go there in winter is a question worth considering. It is on the edge of the world, the northernmost town in Europe, as far from London as London is from Tunis, a place of dark and brutal winters, where the sun sinks into the Arctic Ocean in November and does not rise again for ten weeks.
I wanted to see the Northern Lights. Also, I had long harboured a half-formed urge to experience what life was like in such a remote and forbidding place. Sitting at home in England with a glass of whisky and a book of maps, this had seemed a capital idea. But now as I picked my way through the grey, late-December slush of Oslo I was beginning to have my doubts.
I decided at the outset to start at the North Cape, the northernmost point of the European mainland, and to make my way south to Istanbul, taking in along the way as many of the places Katz and I had visited as I could manage. My intention had been to begin the trip in the spring, but just before Christmas I made a phone call to the University of Tromsø, the northernmost university in the world and hotbed of Northern Lights research, to find out when the best time would be to see this celestial light show. The phone line was so bad that I could barely hear the kindly professor I spoke to – he appeared to be talking to me from the midst of a roaring blizzard; I imagined a door banging open and swirling snow blowing into his frail and lonely hut somewhere out in the wilds – but I did catch enough to gather that the only reliable time to come was now, in the depths of winter, before the sun rose again in late January. This was a very good year for Northern Lights, as it happened – something to do with intense solar activity – but you needed a clear sky to see them, and in northern Norway this could never be guaranteed.
‘You should plan to come for at least a month,’ he shouted at me.
‘A month?’ I said with genuine alarm.
‘At least.’
A month. A month in the coldest, darkest, bleakest, remotest place in Europe. Everyone I told this to thought it was most amusing. And now here I was heading north on a bouncing bus, inescapably committed. Not long after leaving Oslo I became aware with a sense of unease that no one on the bus was smoking. I couldn’t see any no smoking signs, but I wasn’t going to be the first person to light up and then have everyone clucking at me in Norwegian. I was pretty certain that the man in the seat across the aisle was a smoker – he looked suitably out of sorts – and even more sure that the young man ahead of me must be. I have yet to meet a grown-up reader of comic books who does not also have an affection for tobacco and tattoos. I consulted the Express 2000 leaflet that came with each seat and read with horror the words ‘tilsammen 2,000 km non-stop i 30 timer’.

Thank you both. Perhaps they will need to rethink

Commenting on the above... I spent about 45 days once in the interior of Alaska during the winter. Right in the belt of highest activity, in one of the drier regions of this vast state. I saw the lights exactly three times, and I had to make a considerable effort on two of those occassions. Only once during this month-plus stay did I randomly look up and see an unexpected light show.

So... you can sometimes get lucky (although this isn't a bet I would take in a casino, if I gambled), but if you really want to see the lights you have to be very patient and persistent.

The Mona Lisa, the Eifel Tour, the Houses of Parliament, the Leaning Tower of Pisa, the Coliseum, Brandenburger Tor... these icons of Europe will always be there waiting for travelers to gaze upon them. The Northern Lights, however, are ephemeral... they follow their own schedule, not your's.

Here is what the Norwegian Tourist Board says:
http://www.visitnorway.com/us/what-to-do/attractions-culture/nature-attractions/let-there-be-northern-lights/when-and-where-to-find-the-northern-lights/

I lived in Stockholm for two years and never saw them.