You should go to Booking dot com https://www.booking.com/district/gr/nafplion/nafpliooldtown.html --put in dates & a list appears. Do NOT start scrolling down the list -- instead, click icon "Show on Map" and you then see all available places as blue balloons, with the price beside each. There is a purple Legend "Archeologiical Musem" -- that is the Main Town Square. ALL the places on the Seaward Side of this are on flat streets ... and also on the street just inland from this, Called Staikopolou. From there inland, stairs go up.
I have some suggestions, but don't know what your chances are. (Nancy, for future reference, if you can give dates, you'll get much b better help-- without them, it's guesswork, and we may supply unhelpful options). Have you checked THE best guide to all aspects of Nafplio?? Where to stay - eat - walk - sightsee - shop -- http://www.visitnafplio.com/ ? Noncommercial; superb -- click Every link! Its creator says, & I agree, that HOTEL AGAMEMNON has Best location in all Old Town... riight on seafront... balconies, 3 floors (w elevator), buffet breakfast in lobby....and moderate prices .. but getting hard to book. Just a block off the atractive marble-paved squar is always reliable Hotel Victoria, balconies, views of the high fortress, elevator. Another attractive choice, a family-owned Omorfo Poli ("Beautiful City") is on quiet lane, next to a museum. Good lulck on all these!