WE used The Croft at Haseley Knob, Warwick a couple of years ago to visit Warwick Castle. Only a couple of miles out of Warwick, not far from the canal. In fact, we cycled to the castle down the canal, had a fantastic day there as it was a jousting event, then cycled home at the end of the day. No parking problems, congestion at all.
The site itself, is well laid out, with security gates. It has showers and toilets and is easy to find. The only downside we had was that it is under the flight path of Birmingham airport. Being out most of the day, it didn't bother us, but would certainly recommend the site.
Its listed under Kenilworth in the CC handbook, tel 01926 484447, or try www.croftguesthouse.co.uk.
Good luck