Chamonix has lots of accomodation and is rarely sold out as such. However the popular budget stuff does sell out early especially the climbers favourites. I would suggest you just call the Tourist Office re apartment rentals. Also quite a bit listed on Air B&B (just check locations for what you want, remember car parking can be tricky and isn’t free). We stayed last summer in the Park Hotel Suisse (very nice) which is more like £120 a night.
Have a good look at the map as Chamonix and the valley is quite spread out. If it is two lads I’d say you want to be in Chamonix itself as its the most lively.
Enjoy people watching the Japanese 😉
EDIT: if you have a car there is a carrefour on outskirts of the town or a more pricey supermarket in the centre, if you are super organised you could stock up at a bigger supermarket down the valley before Chamonix somewhere.