An example of a Folly located in Bath, England, Ralph Allen's Sham Castle (I've never heard anyone locally call it that - usually it's just "Sham Castle" but it's not the only one in existence) was constructed in 1762 purely with the purpose of enhancing the view from Ralph Allen's townhouse. From there and many other points in the town the castle can be seen up in the hills through a clearing of trees and appears to be the genuine article.
However, a visitor to the castle itself will find just the front wall - and this is by design, not dereliction. Whilst building an entire castle would have been truly foolish, at least constructing merely the front for the appearance of a castle is a more practical way of achieving the desired effect. The downside is that less effort was put into the back of the structure - it's considerably less realistic and makes the whole artifact seem like a movie prop or an oversized lego piece.
The construction was by Richard Jones and inevitably used the characteristic creamy-coloured Bath stone - even now it's hard to find something here constructed out of materials other than this stone itself or imitations of. It was financed by the aforementioned Ralph Allen, who had become Postmaster of Bath at the age of 19. He made his fortune by introducing several innovations to the still-young postal service and then shrewdly invested his payment in land in the surrounding area. In particular, one such area was Combe Down, where the bath stone is found in abundance and from which much of the city, including his mansion, Prior Park, was constructed. Today, the Castle has been altered by the filling in of the "windows" (of course, there were no rooms behind them) and the addition of a plaque dedicated to Richard Ottloy and Arthur Withy, who in 1921 carried out considerable restoration work.
Whilst the intention was to enhance the view from the city, the reverse scenario is actually more impressive - looking down on the whole of Bath from a considerable height (Bathwick hill is not for the faint-hearted, and is, I'd wager, the reason buses up to campus run until 3AM - no drunk student would manage it) is fantastic during the day but even more so at night(1) -although at certain times of the year halogen floodlighting spoils the experience slightly. The Castle is a very short detour from the route of the Bath Skyline Trail. Access can be obtained from the university or, more immediately, the golf club (although that's technically private). Certainly, I've found it provides a calm refuge away from the bustle of university and city without also feeling remote.
(1) As a student at Bath, I owe my discovery of Sham Castle to the night the hour changed back for winter- one of my housemates had found it on a map earlier and we reasoned that if it turned out to be nothing special, the hour rolling back would mean that we effectively lost nothing by going there... So it was that I found myself setting out with an assortment of students in various states of drunkenness (myself sober, but with no more idea of how to get there than the rest, or anything useful like a torch) at 1AM to a fake castle. In fact, it was quite an experience- it was so dark that you couldn't see your own feet (nor did we notice the castle until we practically walked into it) yet the city spread out beneath us was gloriously lit. The other advantage of going at night is you can't see the one thing that spoils the view, namely the gasworks. Also worth it for a confused housemate wandering into the kitchen the next morning to ask "Did we actually go walking through fields at midnight to find a fake castle, or was I really stoned?"
(A version of this writeup appears on SoSauce; I am the contributor of both)