This will work because you're not duplicating mass amounts of text. You won't be penalized for duplicate content unless you really copy something of substance.

That being said some points I would note:

1. Don't duplicate descriptions, reviews or comments, wait until you gather your site gathers its own comments/reviews (or make some, if you're sneaky).

2. So you write a script that extrapolates information about establishments from a couple of large directory sites (based on their layout) and populate your own database.
Do you realize that if your server does this in bulk, you may use a great deal of bandwidth from the target site and they may personally penalize you somehow, or launch a complaint? If you're flagged as malicious, Google won't want to to touch you with a ten foot pole.
To circumnavigate this, write a time-delay into your extrapolation script or run the whole thing from [a] remote server[s] (it's kind of black hat, I know).

3.When you design your template page, make sure it looks nothing like the pages from whom you're pulling the data. Change the name of the fields a little, Stir the design and style around so it has some originality to it. Google shouldn't care about this too much, but it's worth considering all the same.

Good luck, what you propose is a massive undertaking.