I envy you that experience, Mike. As a matter of interest, it's reckoned that the maximum number of stars visible to the naked eye from a single location is about 4500, assuming you can see down to magnitude 6.
"billions and billions" is an exaggeration of course, but I assure you from the observatory on la Palma you can see far, far more than 4500 with the naked eye. It is impossible to describe in words - totally awe-inspiring. You don't need binoculars or a telescope. Remember this is above the cloud layer. It's one of the prime sites for astronomy in the Northern Hemisphere, which is why so many telescopes are sited here.
La Palma itself is beautiful - it's not a big tourist destination with concrete horror resorts like the other Canary islands. It's essentially a diamond-shaped island divided by the Caldera de Taburiente in the north (where the observatory is) and the Cumbre Vieja, a line of volcanoes that form the spine running north-south. It has a variety of landscapes ranging from lunar in the south (Teneguia, which erupted in 1972) to lush tropical forest (Los Tilos) in the north and several microclimates. It's a good location for hiking and scuba diving. It's quiet though - not one for party animals. There are beaches at Los Cancajos, Puerto Naos (black sand!), and Tazacorte. There are open-air sea pools at Charco Azul and La Fajana.
The locals are friendly (friendlier once they realise you aren't German - the Germans are not popular). A smile and a few words of Spanish will go a long way.
The Fiesta de Diablo in Tijarafe (8 September every year) is a must-not-ever-miss if you can cope with the drive up and down a perilously steep valley in the dark at 3am with a local in his jalopy attempting to get intimate with your rear bumper. Don't go if you don't like fireworks, particularly in close proximity https://www.youtube.com/watch?v=p05NveiKV9o
If you want a La Palma treat ask in any bar or catetería for "un barraquito con licor" - coffee, cream, liquor ("cuarante y tres"), milk, a slice of lime peel (no peel = it's not a barrquito). Should be served in a glass, ideally with the layers distinctly visible, not mixed together. Sounds horrendous but is to die for.
The airport code is SPC (make sure you're not buying flights to Las Palmas, which is on a different island!) and Thomson fly direct from Manchester and Gatwick. Flight time 4.5 hours. The approach to the airport is, um, "interesting" - over water right until the last minute, and the runway is short. A hire car is essential.
The road to the mountain top (Roque de los Muchachos, 2500m altitude) passes through the observatory and you can see all two dozen telescopes, though you cannot go inside except on official open days - there are people working in them. Drive time from the capital, Santa Cruz, to the peak is about an hour. The road, although paved, is twisty and dangerous with several steep, blind hairpin bends. If you're really lucky you'll enounter one of the buses bringing tourists down and have to reverse back to a passing spot - bearing in mind there are few barriers between you and a loooooong drop before you hear the splash. There are several "miradors" - beauty spots - on the way up where you can stop, calm your nerves and have your breath taken away by the view. Take suncream - high UV at the top because of the thin atmosphere and you will burn fast.http://www.telegraph.co.uk/travel/sunandsea/9867981/La-Palma-guide-the-forgotten-Canary-Island.html
Merry Christmas one and all!