You will be right next to the Galata Tower. Walking distance to many interesting parts are very close. For more restaurants walk down the hill, 7min, to Koroköy. Crossing to Eminönü is a 10min walk over the Galata Bridge. You literally dont need to go to a Roof top bar - the veiw from the roof of the building is sensational.
PCR Test can be done 200m from the appartment at the Austrian Hospital. Cost 30USD, all procedure takes 10min per person and we got the result (offical docuemnt) within 12 hours through email. I think they do not open on Sundays-