Well, around 100$ per night...and it should be within walking distance of the corniche and the souks...but I think I found a good one.

http://dohasafeerhotel.com/enquiry.html

Looks good to me, good price as well :) So I safe enough to invite you for tea, Mila ;) 

Doha, I'm coming! Ducks in Doha from 12th - 18th of May :)