It's highly likely you'll find yourself blocked by the competitor in question. Not right away, but as soon as you get noticed, they'll start squeezing you out, or block you outright.
They have no legal obligation to provide you with access, and since you're a competitor, they can demand licensing or fees as compensation for using their resources. I do not recommend taking that approach.
If you must, then have a fallback in place. Use the competitors data while it's available, build your user-base, and stock your own db tables with the data you need in order to provide the service. Determine ways to obtain this data yourself, and start building the tools / services to obtain that data.
It's not a sure-fire way to launch your business, but it at least won't leave you completely dead in the water when yelp or opentable pull the plug on you.