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I have a whippet and he's lovely, he could cope with 1 hour of walking a day but gets more like 2 hours a day and benefits from that. I don't think there are many breeds that need less though, so a whippet would be a fantastic choice.
I think @Velocio will struggle to find a rescue that will rehome to someone living in a flat. Nowhere let us adopt because our garden is not fully enclosed - personally I think that's madness, our dog has a great life, but all the rescues seem to have very strict rules and no leeway.
I'm not tied to a breed at all, but a large dog would be inappropriate for the size of the flat and my current weekend habit of driving out of the city and going for an 5-8 mile walk in the country is better suited to a medium dog that isn't excessively docile.