I heart Reykjavík
I Heart Reykjavik should be your GO TO for Iceland. Their website has everything you could imagine and they respond promptly to questions via email. I have never used a travel agent because I don't like third parties and I like to control my vacation. I emailed I Heart Reykjavik with a gigantic blurb about what I wanted to do in Iceland. They responded promptly with paragraphs of suggestions and links for tour options. I put my trust in them to book everything for me and they followed through 100%. All of my tickets were emailed to me with clear instructions and they even made a last minute change with no complaints after I completely forgot to tell them I changed my hotel (and this was like the night before I arrived). Furthermore, during one of my tours we were delayed a bit and I emailed I Heart Reykjavik and they responded right away with options for solutions if I didn't make it to my next pick up on time. I totally trust I Heart Reykjavik and the partners they choose for the tours - I had an incredible time during the two days I was in Reykjavik.
Regarding the walking tour they provide - this is the PERFECT thing to do after you land and I'm so glad the timing worked out for me to do just that. I have to imagine that they wouldn't hire anyone who wasn't a great tour guide so regardless of who takes you on the walking tour you should learn a lot. Personally, I LOVED our tour guide, Villimey, and I'm so happy she was the one to show me (and a few other people) around downtown Reykjavik! She has a great personality and clearly loves the town. I also appreciated her story about her name and loved getting hot chocolate at the library and talking about Harry Potter and tattoos.
I digress - the reason you need to do this tour first is so that you know where to go! Based on I Heart Reykjavik's recommendations I had the BEST coffee, ice cream, and cinnamon roll in town. I knew where to go for food or drinks (if I would've had the time) and I learned that you could go to the top of Hallgrimskirkja Church (which I totally did after the tour). During the tour we were given the option to use a restroom multiple times, we took breaks from walking to appreciate street art or a view, and afterward Villimey stayed around for questions, directions, and/or further recommendations.
Do not miss this guided walking tour of Reykjavik!