Just spotted this, so may be too late. We stayed here, basic but cheap with secure parking. Only a couple of minutes walk from old town centre. Pansion Stari Grad Bijelina Cikma 4, Sarajevo 71000, Bosnia and Herzegovina
You can check Tower House (Hadzisabanovica 15, 71000 Sarajevo) , also Hostel Hayat (Abdesthana 27, 71000 Sarajevo).