I would suggest anywhere in the greater Reykjavik area. Do not book for Thursday night we are not in Reykjavik!
Try booking.com or similar for hotels, that’s the cheapest option. If a smaller establishment, find their name and email direct, save them the 20%+ commission.
If I know of the dates and arrival, we can supply a shuttle service, small fee for fuel, and I can approach a hotel we use for the last day, they have suggested they would offer the same rate. 4 star hotel.