I found a site on the east side of Cardiff last week and landed there. Had a really nice welcome and there is enough room on the front lawn by the fountain. Take a look:-
St Mellons Hotel - Luxury Country Hotel Between Cardiff & Newport
If you want somewere on the west side of Cardiff then you have
http://www.miskin-manor.co.uk/ a dedicated helipad there to the south of the back lawn, and the owner Colin is a Helicopter pilot himself. again you always have a nice welcome.