It is easy and (relatively) reasonably priced to see much of England and Scotland relying solely on public transit from the major cities.
Many people overspend on private day tours or rent expensive rental cars, mistakenly believing that is the only way to see many sites. While private day tours may sound appealing, they allow for less freedom than you'd expect and, if you're like me, you may end up stuck with a guide providing more commentary than you'd actually enjoy. Also, if the best part of a day trip is visiting the local pub (which it is), I'd rather do this without someone waiting in the car.
Top 10 easy U.K. day trips relying solely on public transit:
NOTE for my American friends: You can drink on trains in the U.K. (after 10 AM - don't be ridiculous). You can even bring your own booze onto the train (they sell small, safely packaged booze in the train station shop, for this purpose).
Money saving tip: It is often significantly cheaper to buy your tickets in advance. That said, sometimes the convenience of being able to change your plans or a desire to take a spur-of-the-moment trip, makes the extra expense worth it!
WC: There are WC on essentially all trains (not on the Tube) and they are the nicest of any I've been on overseas. I've only been on one that had run out of paper (ONE!!). The stations also generally have free WC, though some of the more remote aren't monitored often.