And Charlotte Square's most famous residents even include a tennis champion - Harold Mahoney - who became the first Scot to win Wimbledon when he lifted the trophy in 1896. He was born at number 21.
It may still be the official residence of the First Minister, who lives at Bute House, number 6, but in the past few decades, the square has lost some of its lustre.
Its large central garden still plays host to the annual Edinburgh International Book Festival, a fixture there since 1983, but the departure of many top legal and financial firms to London or to purpose-built offices elsewhere in the city has meant the grand Georgian square is no longer the business and financial hub it once was.
That may be changing, however. The wrapper has just come off a £12 million renovation project that has turned six townhouses on the south side of the square into four elite office complexes complete with a glassed-in atrium and a new four-storey block on Hope Street Lane complete with underground parking. The development occupies buildings once owned by the National Trust for Scotland (NTS) and sold by it in 2009 in a controversial £8.8 million deal that saw NTS relocate to the outskirts of the city.
The redevelopment was undertaken by Edinburgh-based architects Morgan McDonnell in conjunction with Corran Properties, which now runs a portfolio of 19 properties in the square under the title The Charlotte Square Collection.
Among the new tenants are finance company Cornelian Asset Managers, law firm Ruffers and Scoban, a new private bank. Other heavy-hitters already in the square include fund manager Walter Scott & Partners.
"The New Town is steeped in local and economic history and as a business address, Charlotte Square offers a level of distinction that can't be matched," said Nick Ball, director of Corran Properties.
"The vision is to see the square reinstated as the prestigious centre of the city's financial community, giving Edinburgh an address that is renowned globally. "
Of course, what every high-class address needs is a statue. Charlotte Square already has one - Prince Albert. Enter Alexander Stoddart, Sculptor in Ordinary to Her Majesty the Queen in Scotland. His monument to physicist James Clerk Maxwell sits at the east end of George Street and he wants to match it with one at the gateway to Charlotte Square. This time the subject will be the man who designed the square in the first place, Robert Adam.