There is ( or used to be) a LCDH diagonally across the street from Starbucks on 5th street. There ( and pretty much ONLY there) you will find genuine Cubans, but at LCDH premium pricing.
5th street is a great street to shop, eat, and buy everything from 10-peso souvenirs to a high end stuff. It't parallels the beach, and it's about a mile long. If you want genuine Mexican food, go to where the locals go: El Fogon...Just ask a taxi driver to take you there.
Have fun!