Tips for what to do whilst in Iceland.
DON'T do the Golden Circle and Blue Lagoon! Sorry too late for you OP, I know, but if anyone else is thinking of going, its not the best way you can spend your time. They are fine and you will enjoy them, but there are better trips and hotsprings which are not so rammed. It can seem like half the city is at every stop you make unfortunately.
If you can afford one big trip, I do recommend Into the Glacier
intotheglacier.is/ Its a full day trip out of Reykavik but worth it.
Personally I don't recommend the whale watching. We have done it in the past, and I'm sure its great if you get lucky and the whales are friendly. Unfortunately the day we went, the visiblity was shocking, the whales did show but you could barely see them and I have never been so cold in all my life and I was well dressed! I stress this: Iceland is cold in the damp, gets in your bones, windy kind of way. Even when +2C. I'd rather be in Swedish lapland at -14C! Honestly, make sure you have thermals and layer up in a big way! If think its perhaps better to take a trip over to Videy Island and the Peace tower if you want to do a boat trip. Less disappointment and cold!
Things to do in Reykavik itself:
Walk up the hill to the church Hallgrimskirkja. Its stunning. You can go up the tower and see views of the city. The walk up the hill is rather lovely with lots of hand crafted gift shops. Look out for the brightly coloured traditional houses. Its a good one to do in the evening, if you happen to be busy the rest of the day.
Laugavegur, the main street, is also a nice walk with lots of gifty shops. I'm not big on buying tonnes of tourist tat, but I do think its one place worth going window shopping. The jewellery shops are particularly lovely. Simple but enjoyable.
Also do take a walk down by the harbour area. There are wonderful views across the bay, particularly on a clear day. Go down to Harpa Concert Hall. Its impressive and looks good in photos!
The little lake in the centre of the city Tjornin is pretty too. Nice to go and simply see the ducks.
If you are unlucky any don't manage to see the Northern Lights on the tour (you don't always), and you can't get out of the city to try again, you can get a taxi out to Grotta Lighthouse. We were lucky enough to see them there last time we went. Its a pretty little lighthouse. Not much else out that way though, as its close to a residential area.
I echo what Chunkymonkey says to book restuarants in advance. Last time we didn't, and we weren't able to get into a few places. The number of tourists in the city compared to a few years ago is huge. We DID manage to get a place by walking in, but you had to try go earlier to do that - before all the coach tours return!
Its not cheap to eat out but I'm yet to have a bad meal in the city. I've always relatively impressed at the food tbh. I recommend having fish even if you normally wouldn't and having lamb even if you normally wouldn't whilst you are there if you can. Iceland seem to excel at both.
Last time we went, we went to Islenski Barinn, which is close to the centre on a side street off Laugavegur. Its a pub style place with food along those lines with an icelandic twist. We went there on our first night, and managed to get a walk it. Its cosy. And good if you like your beer (and can cope with the price of alcohol in Iceland!!)
Tapas Barinn is an icelandic style tapas place. Which let you do a few different traditional icelandic foods all in one meal. I think there are a few similar places. Its not somewhere to go if you want quiet, and like everywhere its not cheap.
We ended up at the Old Iceland Restuarant one night. It really wasn't our first choice but it was about the fourth place we'd attempted to get in, and we were fed up by that point. It was better than we'd hoped tbh. I did enjoy it.
We've did go to other places last time we were there, but I can't for the life of me remember the names of them. But as I say, I do think the quality of food is pretty damn good in most places.
You'll have a blast OP. I love the place and its one of the few places I've been multiple times, and would go to again in a heartbeat.
Enjoy!