A lot of nice hotels are downtown Reykjavik close to Harpa like:

Hotel Reykjavik Centrum:
http://www.hotelsoficeland.is/our-hotels/hotel-reykjavik-centrum

Hotel Centrum Arnarhvoll:
https://www.centerhotels.com/hotel-arnarhvoll/

Hotel Centrum Plaza:
https://www.centerhotels.com/hotel-plaza/

101 Hotel:
http://www.101hotel.is/

Radissonblu Hotel 1919 Reykjavik:
https://www.radissonhotels.com/en-us/hotels/radisson-blu-reykjavik-1919

Grand hotel Reykjavik:
www.grand.is

 

And many more... just google it!