Radison blue Hótel Saga is an excellent upscale place to stay near the center of the city. There is also Hótel 101 which is right down town.
Other great places are Hilton Reykjavík Nordica and Grand Hotel. There are also smaller hotels like hotel Reykjavík, Hotel Holt (Which, even though its smaller, is not cheaper nor less grand. It also is right down town) and Hotel Arnarhvoll.