There is an area downtown Raleigh called Moore Square you might enjoy.
Moore Square :: Downtown Raleigh, NC
There are a lots of restaurants and bars and a museum with Imax right there. Also lots of street and parking garage spaces that are free on the weekend. You could just park and walk around and see what looks good to you. There is a Segway Tour company right there, if they had an opening you could take a tour of the city. Friday and Saturday are calling for rain but you never know how it will be.
When I have guests they like to visit the local colleges...NCSU, UNC and Duke are all right here.
There are a bunch of meetup activities going on around town you could see if any interest you.
There is a trolley that does 1 hour tours of downtown Raleigh for $10 and you can hop off and on at the stops.
The Art Museum is maybe 2 miles from the staduim for your hockey game with free parking and free general admission. It was just remodeled and expanded, and part of the Greenway walking path goes right through there if you are a walker. There are a few peices of art along the way.
Hope you enjoy your visit!