Cuba is extremely safe. Guns are illegal and drug crime is not prevalent.
I explored the streets of Havana alone with no issue (apart from vendors and cabs calling out their services, of course!). Any type of traveller — including solo and even the not-so-adventurous — will feel completely comfortable exploring the country. However, as with anywhere in the world, particularly cities, there is petty theft, pick pocketers, etc. As a tourist who may or may not stick out (and who is probably carrying a lot of cash), be a smart traveller and stay aware of your surroundings. Plenty of your new Cuban friends will most likely look out for you as well!
Image Source: POPSUGAR Photography / Hilary White