A couple of possibilities (both with good reviews):
Cosmopolit Hotel: 5 minutes walk from the Acropolis, air con, free wi-fi, TV, en suite facilities, breakfast included, double/twin rooms at £52.88 per night (per room, not per person).
Evripides Hotel: Close to the Acropolis, air con, free wi-fi, rooftop bar, en suite facilities, breakfast included, double rooms £61.69 per night.
Both found on my favourite accommodation site:
http://www.hostelworld.com
[NB: Don't be put off by the word 'hostel' in that URL. There are some lovely hotels and B&Bs there too. Simply carry out an initial search and then use the filters to select the types of accommodation you're interested in, followed by using the 'Order' option to put those closest to the centre of Athens at the top of the list. I found a superb little hotel in central Madrid on that site a few years ago, with TV, wi-fi, air con, etc, for just €22 per night!]