I wouldn't park long-term on the street, but I've seen quite a few pictures from people here who cover the car and park it on a private driveway / lane. If you're in a nice part of town, I don't see how carefully covering the car and putting it in a secure, paved off-street parking place will do much harm beyond maybe leaving some swirl marks on the paint from dust under the cover.
I wouldn't leave the car uncovered outside for a length of time though, especially during a rain storm. These cars don't drain water from important areas, and even without precipitation all of the vents and louvres will pick up leaves and dust like nobody's business.
One thing to consider is insurance. Some companies charge more for cars that aren't garaged, and if you fudge it and then try to get a vandalism claim covered you'll be SOL.