As mentioned above, Loch Lomond and Glasgow are relatively close to Hunterston but there are also many other tourist sites - Culzean Castle being one. (40 mins away)
North of the plant is Largs and south of the plant is West Kilbride, Ardrossan, Saltcoats and Stevenston.
Depending on the time of year, there are Highland Games festivals throughout the area. The Ardrossan Highland Games are the 2nd weekend in June every year.
The Johnnie Walker distillery is in Kilmarnock, about 30 mins from the plant.
A lot of Open Championship golf courses are closeby also - Royal Prestwick, Royal Troon, Turnberry, all less than an hour and many more affordable links courses to play.
There are many pubs in the area (probably too many), especially in Largs and Saltcoats areas and they mostly all serve food also.
There are Bed and Breakfasts in all those small towns and probably the nicest (but most expensive) hotel is the Seamill Hydro less than 10 mins from the plant.
The US Navy base at the Holy Loch is just north of the plant and the subs can sometimes be seen out in the Firth of Clyde, where the plant sits.
Like South African says, Arran is a great place to visit for a day, especially if you like hiking (or golf). There is a car ferry that leaves Ardrossan Harbour. From Largs you can take a ferry to Millport, on the island of Great Cumbrae... little town on a little island with a few pubs and restaurants.
Best places for shopping are either Irvine, Kilmarnock, Paisley or Glasgow. There is a mall (Braehead Centre) between Paisley and Glasgow.