Single journey car rental

I'm not aware of any car rental agency that won't expect specific details about the place and time of your return.

You will need to give a specific location, date and time for where/when you will return your car. If you fail to show up there, more-or-less when you say you will, you will have some trouble. Show up a few hours late, they'll probably just charge you for an extra day. Don't show up at all...that'll cost you more.

FWIW, those expectations seems perfectly reasonable to me - if I let someone use my car, I'd expect them to honor the contract (a legal promise) they signed that specified where and when I'd get it back, too.

If you don't want to be locked in to a return location/time, I think you have a couple options:

1) Pick someplace that you're confident you could reach after you've finished your meandering and pad the time (so you can get there after meandering); or
2) Don't rent a car. Consider leasing one (more complicated, but will also come with expectations for return so maybe no better) or, buying one (infinitely more complicated, and maybe not at all practical, but an option that would give you greater freedom, although it would come with plenty of significant complications at the end, too).

Bottom line: renting a car buys you a lot of freedom, but it also comes with responsibilities.

While you have to select a drop-off in advance, the contract will usually also provide phone numbers and instructions for changing the plan, if necessary. You obviously want to choose an agency with lots of locations.

I can't speak of Hertz UK , but Hertz USA was good at being flexible when the Spousal Unit's mother had her final illness on the other side of the country- every night he'd call to extend the rental another day and was told he was good to go, and he even got the one week discount rate when he hit the seventh day.