Some obvious locations mentioned already, but if the weather's ok, just wander around! Wonderful place. It has soul, and a sense of being solidly rooted in the landscape.
The older I get, the more I appreciate the solidity of places which have clearly being around for many generations. They remind you that we're just cogs in the much bigger wheel driving human history. Modern towns and cities just make me feel like fuel being burned in the engine of progress.
So, er... yes. Go gawp at the Minster and walk the walls.
I resent having pay to go in a house of God.
I know what you mean, but as a hardcore atheist I grew to understand the financial pressures these places are under, and you only have to wander around a few to realise just how expensive it must be to keep such marvels going in the modern age. No slave labour to draw on! Not now the Poles want decent wages, anyway.

So just look on it as paying to see the medieval equivalent of the space race. These are the Saturn Vs and Space Shuttles of previous generations, and they are every bit as marvelous. Especially when you look close and find the marks of the men who, centuries ago, risked life and limb to build them.
So breathe deep and empty your wallet. You know it's worth it really.
PS Having said that, they're taking the Micky at Westminster Abbey... £18. Tourist trade ripoff.

I prefer to wander down the rail line to Rochester and make a £5 donation when I feel the need to immerse myself in a bit of calm and history.