Name change - I am the OP.
I'm back! I had a great time and would thoroughly recommend Reykjavik as a short break and (from what I saw) the whole country for a longer break. He's a brief summary of experiences that may be useful to other travellers.
Food
Generous portions, very tasty, service very good. Bread and chips/fries were very salty - this seems to the norm. They're very keen on salt rubs.
Prices, food and drink
Yes, it's very expensive. You can't get anything for less than 1,500 KR, which is around £10. But it's worth spending more for dishes like:
Fish and chips (though I actually had battered broccoli and cauliflower instead of chips) from the Icelandic House on the harbour. Absolutely delicious.
Famous lamb stew / broth at the Cafe de Paris - just what I needed after a day's horse-riding
Cafe Uno in the harbour square is also good - I had a great stead salad there.
I don't like hot dogs so I didn't try the 'famous' hot dog stand. a
Drink - I like a cold lager with my meal, but again, a bottle started at around 1,200 KR (£8 +). However, if you look at the Soft Drinks section on the menus you will find a Pilsner or Gull at around 2.5% alcohol, and these are half the price of the normal beers / lagers and - to me - taste just as good.
Accommodation
I stayed at the Metropolitan Hotel. It was very basic - think small student room with no frills, except ensuite. TV, single bed, desk, mirror - that's it. No toiletries provided. It was fine though, because I knew what to expect and the location is fabulous. The harbour is about 3 minutes away and I wanted to be right in the centre.
I booked breakfast, which again was basic but it did the job. On the last day though I got downstairs at 8.10am to find no breakfast and just one other woman in the dining room. After we'd tried ringing the hotel number and got no answer your intrepid traveller went into the kitchen and found the fridge, where everything had actually been put on platters the night before. So the two of us carried everything out to the dining room and tucked in. When I went back to collect by bag later - which I'd had to leave unattended in reception - it turned out that the day manager had overslept....
Excursions / transfers
I used Flybus for airport transfers with pick up and delivery to my hotel - this is what everyone seems to do and it works very well.
Riding - I was too ambitious. Not having ridden for 5 or 6 years, to book a 40k trek was too much. I did it, but the last 2 hours were not especially enjoyable, and we had to mount and dismount around 6 or 7 times during the day. I was most disappointed about not cantering at all, but this was my fault really for not checking beforehand. Instead it was either walk or the Icelandic 'Tolt', which is supposed to be super-comfortable (it's a fast trot, which you don't rise to), but i found extremely uncomfortable.
Also I got a horse that just wouldn't go! And being told to 'keep up' several times I finally said I found the mare difficult, only to be told by the leader "Yes, she has a reputation for that. You have to really make her work!" Not impressed.
The Golden Circle was great - a lovely day visiting scenic beauty spots.
Let me know if you have any questions. If I think of anything else I'll add it.