Alongside the health sciences, Cuba's already growing tourism sector is the most obvious target for a market economy. The small country is already having trouble providing hotel rooms to the 3 million visitors it receives each year. Once more Americans are able to enter the country, the need for rooms and other amenities and services will only grow. "They need everything," said Jonathan Blue, chairman and managing director of Louisville, Kentucky-based Blue Equity, a private equity firm. "There is not an area they don't need, and now they have the ability to pay for it and want to buy it," he said.
Read MoreBefore you book: A look inside Cuba
Even Silicon Valley-backed lodging start-up Airbnb has moved into Cuba in a sizable way, with 1,000 listings in the country since last December.
Norwegian Cruise Lines already has plans in the works to bring curious tourists to Cuba on its luxury cruise liners if the embargo is lifted. The company wasted no time charting out an itinerary it will market to vacationers looking for a Cuba-focused cruise experience, said CEO Frank Del Rio at the recent Cuba Opportunity Summit in New York City.
Investors looking to make a buck in companies connected to Cuba should consider the leisure, gaming and lodging sectors. "Investment in those type of companies will be the quickest road to appreciation for the retail investor," Hill said.
The influx of tourists to Cuba also means more construction, from better roads to more accommodations and improved access to the Internet and telecom. Building materials, electrical components and heavy machinery will all need to be imported to Cuba, which is good news for the further development of the port. Currently, to get materials into Cuba and then distributed with virtually no logistics infrastructure other than for agriculture is a challenge. "They are starting from scratch," Blue said.
Cuba could also potentially become a competitive player in the sugar, nickel mining, fishery, tobacco and spirits sectors.
But Hill said, "It's a country of 11 million people, so I don't know if it will scale." He added, "I think it's going to be a long time before we see a Cuban stock market."
Herzfeld is more optimistic. His investment advisory firm has already created a private equity fund, the still dormant Cuba Fund, which will look to make direct investments in Cuba as soon as the embargo is lifted.
—By Leslie Kramer, special to CNBC.com