We have a week's holiday the first week in January. We decided on the Canary Islands because of weather. We are interested in historical sites, hiking, beautiful scenery, good resturants and some shopping. Please give recommendations - also recommendations for moderately priced hotels would be very welcome.

Historical sites in the Canary Islands? I'm afraid there aren't. Although Puerto de la Cruz (Tenerife) is a nice town.
Hiking and beautiful scenery, yes! That is, if you stay away from the very touristy places like Playa de las Americas (Tenerife) of Playa del Inglés/Maspalomas (G.Canaria). Lots of shopping opportunities on both islands. Lots of tourists, too!

There are Historical sites in the Canary Islands !! Not as many as in other places, but there are some and you will visit them very quietly because tourists usually don't go to the Islands to see them
Take a look at the Tourist Office website :
http://www.canarias-turismo.com/en/main.php
I think you will like Tenerife better for hiking.

Go to Tenerife, it is more varied: moon-like in the south, lush and green in the north. There are lots of good hikes in the north, east, and Teide mountain areas. Also good, detailed hiking maps.

And there are historical sites, for example the whole center of La Laguna, a little university town with an old center. It is on UNESCOs World Heritage list. I was once there when it was Unesco Day, and all the old buildings were open to public for free.

No Doubt, Tenerife.

Only been to Gran Canaria, it was the worst place we have ever been to in our lives. The place is a dump.

Full of English pubs with scotish blokes trying to drag us in to the restaurants for breakfast.

I cringe just thinking about it.

However on a positive note maspalomas did look a little better but its near to Playa de Ingles which is the epitomy of dreadful in my humble opinion.

The sun was nice though if you can find it amongst the big fat tattood pint drinking,football shirt wearing women.

;-)

Oh yes and its like being on the moon.

So I didn't enjoy it there too much...

Muck

Both islands are really beautifull, but I preffer Tenerife over Gran Canaria.

If you are still looking for a nice accommodation, I can recommend Holiday Velvet. I have had very good experiences with them, and they responded very quickly to my wishes.

http://www.holiday-velvet.com.

This company is active in all the great holiday destinations all over the world, including Tenerife and Gran Canaria. See the following links:

http://www.holiday-velvet.com/tenerife
http://www.holiday-velvet.com/gran-canaria

Hopefully this helps you in finding the perfect place to spend your vacation.

We have been to Tenerife and stayed just outside Puerto de la Cruz, here: http://www.fincaelrincon.com/

You can take the trip up Mount Teide. The landscape round the volcano, which at over 12,000 feet is the highest mountain in Spain, is realy wierd and fantastic. There is plenty of interesting hiking in the north of the island.

Puerto de la Cruz is a tourist town but has a more Spanish feel than the purpose built southern beach resorts. There is a nice botanic garden in there, apparently one of the oldest in Europe, with all sorts of exotic plants growing outdoors. There were also some nice terraced gardens and some old Canarian houses with carved balconies in Orotava and the hotels and houses all had colourful gardens too. We didn't go near any of the big southern resorts, when we were in Tenerife, they really don't look enticing to me.