It seems most travellers don't stay in Nairobi city centre presumably due to safety concerns, opting instead for the outer suburbs. But there are an abundance of cheap hotels (1000 - 2000 KSHS for a room with a double bed and ensuit) around River Road and I felt completely safe there.
I stayed at Hotel Arizona's, which is along River Road, next to the Consolidated Bank entrance. Tel: 0720 852 721. It was a lovely big clean airy room with reasonably wifi in the room. I bargained the reception down to 2000 KSHS per night including breakfast (down from 2200 KSHS) but beware that I was quoted a few different prices by different receptionists so taking a commission is certainly not below some of them.
I walked around at night to restaurants in the area and didn't have any problems but Hotel Arizona's (and many of the other hotels) has a decent restaurant and bar in the building too.
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