Mykonos is not Greece. That was the message from businesses in the windy island of Mykonos, best known for its breath-taking ocean views and vibrant nightlife.

At Nammos, the hottest daytime restaurant/club in Mykonos, the champagne was flowing, house beats were thumping and 20-somethings danced on table tops in bikinis and swim shorts. Prices were steep - about 15-20 euros ($16-21) for a cocktail. But that didn't stop tourists from trying their luck at getting a reservation. The average waiting time for lunch was 2 hours last Friday.

"Mykonos is in its own bubble. Tourists continue to vacation here...despite concerns over Greece's financial state," said Jacopo Janniello Ravagna, owner of Caravana Montacristo, a boutique that specializes in bohemian chic clothes and leather tasselled handbags. The shop was bustling with Australian and British tourists at the time of the CNBC interview.

"Life is fine...and business is good," said Milena Spata, owner of Luna, a handmade jewellery shop tucked away in the little Venice neighbourhood of Mykonos. Spata says business is up 20 percent this summer from last year.

Unlike Athens, no protests or riots have emerged in Mykonos. In fact, Spata's comments were echoed by several shop holders on the island - suggesting that Mykonians were trying to rise above and focus on life on the beach.

When asked whether they voted in the recent referendum on the creditor's austerity measures, most said they voted "yes," indicating that they do care about Greece's role in the euro zone.

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On the surface though, folks in Mykonos are trying to distance themselves from the political and financial drama playing out in Athens...but that doesn't mean business hasn't been affected.

Scorpios, a beautiful beach club and restaurant opened just eight weeks ago on a private beach in Mykonos, has already had to change its menu thanks to the capital controls on transferring funds overseas. The banking restrictions have made it harder for Scorpios to sell foreign beer, wine, tomatoes, mushrooms and seafood, founder Thomas Heyne told CNBC.

Another beachside restaurant in Mykonos said they haven't been able to serve French and Italians wines to guests for the last three weeks. "We've been trying to aggressively market Greek wine and liquor...but that doesn't always go down well with customers who have a refined palette."

But with banks reopening and a deal moving forward between Greece and creditors, business owners were confident they'd be able to serve imported items soon. "It's a priority for us," said one Greek business owner.