Most activities are around Lake Chautauqua. There are several marinas to rent boats. Also there is a nice public beach at Westlake. The Dunkirk lighthouse is also cool.
No zip line that I know of, maybe at Peak N Peak ski area? I'm pretty sure there is horseback riding.
You can go shopping in Lakewood/Jamestown. Depending on the time of year you may be able to rent boats/kayaks on chautauqua lake.
Thanks! Your answer is awaiting moderation.