Are you sure about doing your own tour? Do you have any experience? We booked through a company and they were telling us about the chaos inexperienced tourists cause on those roads after dark. We saw it for ourselves too. Cars just pulled over to the side, and you can't see them until you're almost on top of them. We had to swerve a couple of times.
A guided tour will be able to take you to places that you won't be able to get to, they are knowledgeable and will do everything they can to show you, whereas you could miss them being inexperienced. We used Time Tours and they were incredible.
www.tripadvisor.co.uk/Attraction_Review-g189970-d2054736-Reviews-Time_Tours-Reykjavik_Capital_Region.html
The hot dog stand will be the cheapest meal you'll get the whole time. We stayed in the Radisson Blu next to it and our room overlooked the stand, we didn't know why there was always a queue and hoardes of mostly Asian tourists taking selfies from multiple angles. Turns out Clinton made it famous. Husband said the hot dogs were amazing.
Go to Dillon's. Awesome whiskey bar.
Budget. And then triple it. We had lunch at the Lebowski bar. Just a veggie burger/fries for me and burger/fries for DH. £50. It's about £10 a pint. £8 for a wrap from the local shop that cost me £2.50 for an identical one in Tesco the next day.
Wrap up warm for your NL tour. I went for thermal underlayer, waterproof/windproof trousers, traditional Icelandic wool jumper and waterproof/windproof coat. Plus gloves, pashmina and Ice Wear hat (bought there) and my Dublin boots.
DO NOT layer your socks or wear tights. Your feet will freeze. Invest in wool socks either there (you can get them everywhere) or before you go. You only need to wear one pair.
Go up Hallgrimskirkja church. Views are incredible.
Go to the Harpa. Feel like you're the size of the ant.
The floor in the centre of Reykjavik has underfloor heating. Amazing as you don't slip, there's no ice. Be careful if you go down to the Viking sculpture. It's not heated down there and is super slippery.
Have an amazing time!