I spent 4 or 5 nights in St. Ives last summer. I enjoyed it a lot. I liked window shopping for art and ceramics. There's a branch of the Tate Museum there; it had an all-ceramics exhibition during my visit. I liked it, but the local painters seemed a bit perturbed.
Public transportation around Cornwall is slow, so you may find your day-trip options a bit more limited than you expect if you don't want to spend a lot of time in transit. Especially if you don't expect to spend much time looking at art/ceramics, I urge you to explore the bus and train schedules to be sure you'll have enough viable day-trips to keep you busy for a week. This is not just an issue when you base in St. Ives; it's a consideration just about anywhere in Cornwall if you don't have a car. I split my time between Mevagissey (which gave me access to the Eden Project and the Lost Gardens of Heligan) and St. Ives.
I also spent a night a few hours' sightseeing time in Truro, which I thought was quite attractive though not on the coast.
Cornwall is extremely popular these days. Lodgings get booked up to the point that there simply is nothing available (or at least nothing easily found online). In addition, there appear not to be enough restaurant tables to meet dinner-time demand in some of the coastal communities. If you do not make a reservation for dinner, you may find it quite difficult to find a place to eat.