Many thanks guys for your replys.
I rang the tourist office, who were also extremely helpful and told me I could park in coach park as it was not so busy this time of year. Indeed we had no problem getting parked here (although I would expect it would be more difficult later in the year). Spent the day sightseeing, did the walking tour, had lunch in the city and had a very enjoyable time.
Thank you for your offer Michelinman, its great to see there are still some good people around willing to go that little bit further to help others.
P.S. We stayed at a nice little sight, Hilltop just outside Dungiven with great views over the Sperrins, £12 per night with EHU.
Cheers Xandra !!