Our travel plans are very flexible, so we'd like to rent a car in Geneva, then return it to an unspecified location at an unspecified date.
That is, we won't know the return city or end date at the time we take out the rental.
Are there any companies which will allow this? All of the car rental search engines I've seen require the Pick Up and Return addresses and dates up-front.
Large car hire companies offer this… but do not describe it exactly in the way you do. Specifically, you can always call them to extend the contract, add new options, etc. In effect, the return date and address are mostly used to calculate the price.
I am regularly using Avis and their FAQ explicitly mentions all this. If you exceed some maximum rental period or the car reaches its “end of life” limit, they will point you to the nearest branch (not necessarily the starting point or planned return address) to exchange it.
What they cannot do however is tell you beforehand exactly how much it will cost you (my guess is that it won't be cheap). Which makes sense.
@relaxed's answer proved to be correct, and I was able to phone up and change the drop-off location easily. The cost was calculated at the time of drop-off based on the miles driven, duration of the hire, etc.
But since I mentioned Geneva in the question it's worth pointing out that while I was free to drive the car into other countries, I had to drop the car off within Switzerland.
(I believe this is because of country-specific requirements like the Swiss toll sticker, and the fact that snow-rated tyres are required within Switzerland over winter, so the car company doesn't allow you to drop the vehicle off in another country.)
