A lot of nice hotels are in downtown Reykjavik:
Hotel Reykjavik Grand:https://www.islandshotel.is/hotels-in-iceland/hotel-reykjavik-grand/
Hotel Reykjavik Centrum:https://www.islandshotel.is/hotels-in-iceland/hotel-reykjavik-centrum/
Center Hotels Arnarhvoll:https://www.centerhotels.com/en/hotel-arnarhvoll-reykjavik
Center Hotels Plaza:https://www.centerhotels.com/en/hotel-plaza-reykjavik
101 Hotel Reykjavik:http://www.101hotel.is/
Radisson Blu 1919 Hotel, Reykjavik:https://www.radissonhotels.com/en-us/hotels/radisson-blu-reykjavik-1919
And many more... just google it!