Matt,
Sandwich and Deal are absolute must-sees on the Kent Coast. They are both very strong golf courses and provide a great compare/contrast relationship. I think you will really enjoy the greens at Deal, which has some very solid long par fours on the way in (12, 13, 15, and 18), and some great short ones as well (2, 6, 17). Sandwich, well, it's Sandwich! The dunes on the front nine are unbelievable, but some of the best architect comes out on the back nine, including the skyline green at the 10th, the wild green at the 13th, the first-rate green complex at 15 (Bernard Darwin was a huge fan), and great back-to-back fours at 17 and 18. The two clubs are very different but both special in their own way.
On the way to Bristol--it's the heathland! Woking has an unbelievable set of greens, though it is not always as exciting from tee to green for others. Swinley Forest is the classic heathland layout all packed in to 6,000 yards. Addington is as wild a golf course as you will find anywhere. Huntercombe in Oxfordshire is Willie Park, Jr.'s first layout that is highly original and strategic while containing only 13 bunkers. Others that folks like include Sunningdale, Berkshire, Walton Heath (36 holes each), Hankley Common, and New Zealand. Each of these places is very accessible through either a phone call or a letter. Addington and Woking are probably the most accessible of the bunch.
Near Bristol is Burnham and Berrow, which is a very fine links with architecture from Colt, Alison, and others. The West Coast is very different from the East and will be a very cool experience. St. Enodoc looks like a great choice (although it's out of the way), and, of course, Ran's favorite layout is Westward Ho!, which borders the two courses at Saunton.
If you did Deal and Sandwich in the East, Addington and Woking in the center, and Westward Ho! and Burnham and Berrow in the West, that would be an excellent and highly diverse six course trip. As Bill McBride says, the golf in that part of the world is a feast. Picking courses is like shooting fish in a barrel.