A trip I've done several times is London to Edinburgh. It's a quick flight and even a quick train during the day but if you want to spend Saturday and Sunday you'd have to get up early on Saturday to catch a plane or train which would get you in by noon.
Instead you take the Caledonian Sleeper on Friday evening and arrive in the morning in Edinburgh, ready to start the day.
Although you won't get the absolute best night's sleep, if you come prepared (sleeping mask + ear plugs) you'll get a very decent night's sleep (better than having to wake up early on Saturday).
It's also fun going to sleep and waking up somewhere different!