I worked for Belfast City Council for a placement year so I was in and out of City Hall a few times, they run guided tours and you can married there if you want, (you may need an appointment though :)

tours run October - May
Monday, Tuesday, Thursday, Friday and Saturday at 2.30pm
Wednesday at 11.30am

June - September
Monday - Friday at 10.30am, 11.30am and 2.30pm
Saturday at 2.30pm

Phone (028) 9032 0202

Web Site City Hall