We are spending two nights in Exeter and then four nights in Truro in July.
You will need a car to get around. You can take the train from London to Exeter and rent a car there.
I took this information below from another good post on this blog:
These places are very attractive - find them on the map and then Google them. DARTMOUTH, SALCOMBE, POLPERRO, FOWEY, EDEN PROJECT, LOST GARDENS OF HELIGAN, TREBAH & GLENDURGAN GARDENS (near Falmouth), ST. MICHAELS MOUNT, MOUSEHOLE, PORTHCURNO (Minack Theatre - curt into the cliffs), LAND’S END (although commercialised), ST.IVES, PADSTOW, TINTAGEL, CLOVELLY, LYNMOUTH, SELWORTHY, DUNSTER. Avoid Newquay! Truro is fairy attractive and being central, makes a good base for touring Cornwall.
Roads across Dartmoor can be ‘challenging' for foreigners. Exeter is worth a look but can be difficult to drive in and out of due to congestion. Plymouth has the quay from which The Pilgrim Fathers set sail for America but the city is not that interesting/attractive.
Regarding driving or not - zoom down on the map and then select street view for some of the places mentioned. Most have tiny narrow streets and as a result, car parks are found on the edge of towns.
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I think your plan is a good one, but give yourselves plenty of time for that LHR-Reading transfer. Our British friends will have better advice about that.
Acraven is usually spot on, but I'll say I didn't like the Eden Project -- just a giant overcrowded botanical garden. Didn't really like the Heligan gardens either, but the autumn weather was bad and we were tired from traipsing all over Eden that morning, so YMMV. I'll join the widespread negativity about Land's End itself, but there's plenty of beautiful coastal scenery to take its place. St. Michael's Mount is good, and there's a boat you can take if the tide's high.
Besides Exeter, I'd suggest Truro as your Cornwall base, lets you drive to either the north or south coast. Cornwall roads are very slow even in the off season, must be worse in July, so allow plenty of time to get around. (One reason neither the Romans nor the Saxons conquered Cornwall is how hard it was to go through multiple north-south ranges of hills. They also produced the little harbors that made fishing and smuggling so important back in the day.)