Laundromat, deffo. Great food and not expensive (circa £10 for a main, and they’re generous portions…)
Reykyavik doesn’t actually have to be that expensive. Nearly all the bars have happy hours at some point in the evening, with a modicum of though you can be buying beer (and most of it really good beer) for about £3 a pint up until about ten o’clock. After that you’re talking £6 a pint which is expensive, but not truly shocking (it’s about what you’d pay in a ski resort for example).
There’s a few hostels that, when we went in them for a beer/coffee/food looked really good. We stayed at an Air BnB place right on the main street.