It is very hard to recommend any specific things for visitors to do and see, as it is impossible to know where to start. (The pubs are a good start). Personally, I think the best way to visit the UK is to get out into the countryside and explore the back roads through the fields and villages (and the pubs). It is very relaxing and can also be a great way to get exercise (and find many kewl pubs), as there a zillions of footpaths and cycleways all over the countryside.
I think the best time to visit the UK is just before or just after summertime in Europe, as the whole place becomes a bit of a tourist circus in the middle of summer, not to mention that it can be quite warm and humid - and many of the old buildings (and pubs) are not air conditioned!!
The worst thing about Britain is that it is very expensive, especially if you prefer traveling on a budget. Beer is reasonably priced, so at least your essential needs will be taken care of. Always budget for a lot more than you could possibly expect to pay before you go, especially if you are coming from Australia or Asia, as the pound is way too strong.
One more thing….
Did I mention the pubs? They are excellently located (on almost every street corner) and a great way to catch up with friends. I have a gnome theory on the pubs - they have evolved as a result of the terrible weather that the UK experiences. Even if you look out the window in the morning and the sky is completely blue, it will usually rain (or sleet or snow) before lunchtime. So this means that people get caught out in the rain before they get to where ever they are trying to go. And there is no better way of waiting for the rain to stop, than having a pint at the local - a beer at the pub. That is why there is a pub on every corner. In summertime, the pubs are even more excellent fun, especially if the weather is good, as the sun sets really late.
Here is a pic of me and an old, old, old friend from Sydney. We have an extreme love-hate relationship as she is always really nasty to me, and she has no sense of humour when I poke fun at her. We are having a pint….