I suggest you park in one of the Council car parks which offer free parking for long enough to finish the cache!
If the Castle Gardens are open they are well worth exploring - the view from the top of the Castle Mound is very good
By answering the questions in order you should be able to find the cache which is located at
N 51 36.1(Y/Z)(W+X) W001 07 WZY
After the final question continue along the path then cross the road carefully
The cache is a small screwtop container with a few goodies