Sugar is still a hugely desirable commodity and will have to come from somewhere. Not having it grown in the Caribbean puts a huge dent in Europe's trade one way or the other. If the mainland is still viable, Brazil would be the most likely main supplier. It may change hands more often than it did IOTL as a result.
If the new world is out entirely, the Mediterranean islands may continue to supply much more. This could become interesting once the Ottomans gobble up a large number of them, resulting in a regular money flow from the Christian countries to the Porte. The European powers might fight harder, though who wanted to support Venice? More likely, disunity prevails and Ottoman sugar plays a role in funding the armies and navies menacing the west. I don't think it would be decisive, but it would certainly be interesting.
A possible direction to avoid this would be Africa. Sugarcane thrives here. Europeans generally don't, which is why the New World was preferred for plantations. African sugar would more likely be a trade good. It could do interesting things to internal economics (absent the large-scale demand for salves, West Africa remains a much more varied and safer place where cash-crop peasant agriculture would be viable as a tax base).
Europe would develop very differently. Spain would still have the mines (probably), but the competitors are facing a much steeper climb. Without the profits from the ridiculously lucrative sugar business, French, English, Dutch and Portuguese engagement in the Americas will be smaller and harder to fund. Especially Britain may see its international role greatly diminished, and the industrial revolution is liable to kick off much later and more slowly.
And there would most likely be no banqueting course, i.e. no sweet dessert tradition today. Absent large-scale African slavery, probably also no cotton plantations, no blue jeans, and no 'Manchester model' of free trade economics.
If you want to go overbnoard with this, imagine a world where industrialisation kicks off in the 1840s in a French-dominated 'sugar beet belt' that reaches from Belarus to the Pas de Calais. Engineers from Belgium, Germany and France travel to established centres of mass production in Bengal and Fujian to learn, sailing past a West African coast whose rentier states are withering in the relentless grip of a demand crisis or traveling overland via Ottoman Vienna whose inhabitants relax drinking coffee while the call to prayer drifts over the city.