Moving inside Nicosia by bus:
From Hotel to Old Town: buses 121 - 158 - 160 - 302 - 304 - 306 - 312
bus stop shown on map :(http://www.geomatic.com.cy/geomaps/?wp=details&map=visitcyprus&id=596607079F3ABDDA8AC7DAF350054814)
to bus stop Archiep. Makariou C (0421) just before Evagorou Ave. Take a right on Evagorou Ave towards city hall and old town
From Old Town to Hotel
Same buses: 121 - 158 - 160 - 302 - 304 - 306 - 312
bus stop Archiep Makariou C (0420) to bus stop Archiep Makariou C (0430). You can use the buses from the main bus station (Solomos Square at the heels of the old town).
Bus schedules can be found at the public transportation company’s page. (http://www.osel.com.cy/home-en) scroll down the middle option named “Find your ways by bus” to find the bus number mentioned above. Find the bus stop (i.e. 0433) and hit the time button.
A warning: The schedule is relatively sparse and many buses stop running quite early. Bus 158 is the one that serves the area more often. But the last one is at ~21:00 towards the old town and at 21:30 from old town towards the hotel. One ride ticket costs 1.5Euro and can be bought inside the bus.
Information about Cyprus can be found on https://www.visitcyprus.com/index.php/en/
There is detail information about the island and things to do and visit. It is interesting to follow the link to map on the upper right corner. Then on the window that opens there is rich menu of options from banks to bars and from landmarks to taverns and taxis. You can select i.e. buses and zoom in Nicosia to find the appropriate bus stops.