How impactful can a city be to a startup?

On a website like groupon were it is centrilized (location based) how impactful and important is the first location the website is launched?

Meaning if an app (again like groupon) launches in Chicago or San Fransisco is there a big impact? Are big or small cities preferable for a bootstrapped startup?

There is a similar questions
Is location important for a startup? and What is the best geographical location to do business?, I believe those question tackles physical location of the startup while I am asking about choosing a city for launching a centrilized startup ...

Well I think you just answered your own question sortof

The website is location based, meaning location being one of the most important factors

That said, this is highly subjective. There are benefits to big cities and small.

Big city benefits of course is access to users, and vendors; when you start a site like groupon, even if you're a sales superstar, it'll be difficult getting businesses on board. If you don't have enough businesses represented, you're not really going to get many users, because they will not yet realize much benefit. Bigger cities solve this, due to access to many more opportunities to represent businesses, thus increasing your chance at signing. The disadvantage is the fact that you're not the only one that realizes this, so competition will be a factor, it'll become a money game, who can sign more sales reps, and get to a business quicker.

A smaller city has a benefit of lower competition, however again there are lower resources. For a bootstrapped startup, I'd suggest smaller cities, hire local reps on "generous commission" basis. Additionally, offer businesses finder's fees.

Good Luck!!