Question: I mean through out the whole show cars are depicted almost exactly the same as cars from our time, except for the lack of wheels. You would think that people 1000 years more advanced than us would be able to come up with a new design.

Answer: 
I say it's nostalgia and marketing...As evidence for this I reference the existence of New New York, Mom's Friendly Robot Company ads and just human nature in general. For every viewpoint, you can use nostalgia to sell it! That, I believe, is the simple, unadorned reason that cars look the same in the year 3000.
The requirements for a car in 3000AD are probably very similar to those of cars today i.e. get people around comfortably, safely and cheaply, so they'll end up with broadly similar designs. Certainly demands of fashion will affect the decorative bits that car designers add to distinguish their models, but until material wealth becomes irrelevant I suspect cars will look broadly similar.