Contrary to one clause of your question, there are a number of battery-electric light aircraft (or what the USA calls "light sport" class) in development, with prototypes flying. This includes both fixed-wing conventional types with single or multiple electric powered propellers, and "drone" style craft using what amounts to thrust hover with electric powered propellers. Flight time is limited, but better with the fixed wing types -- enough so that I'd call an electric motor glider a very feasible design.
Hydrogen has limited usefulness, for the same reasons it doesn't work well for cars: it's technologically difficult to store enough for reasonable range. Either extreme pressure, extreme cold, or a chemical storage method that limits the rate at which you can draw fuel are reqired.
A submarine type nuclear reactor was operated aboard a modified B36 in the 1950s -- the project, intended to lead to a strategic bomber with a flight time of weeks or months, was dropped due to lack of need as well as cost and safety concerns (most of the safety concerns, such as "roll-up" explosions, were later resolved or found to be overblown). This kind of power isn't "fully renewable" anyway -- fission fuel must be mined, it isn't grown.
Algae fuels, as drop-in replacements for kerosene, may have some usefulness, but there are storage issues (hard to stockpile something that can mold or rot) -- as you note, however, testing is in progress, and we'll know in a few years.