Bismút is a small espresso place and not a big coffee shop. You can sit and chill but probably wouldn't stay for long. They serve really good espresso from a roaster called Kvörn.
hverfisgata 82 unit 1, 101 Reykjavík, Iceland
Roasters (formally known as Kaffismiðjan) roast their own beans inside the coffee shop. Really high quality stuff and a nice cafe where you can hang and work for hours.
Kárastígur 1, 101 Reykjavík, Iceland
Kaffitár is a large roaster and have a really good selection at great prices. Not a big fan of their house blend but definitely where I would go and buy my beans.
Bankastræti 8, 101 Reykjavík, Iceland