Has anyone any recommendations for a TV antenna (for terrestrial TV transmissions) that can be used on a boat where the signal strength is not good - preferably an omnidirectional antenna.
I'm afraid you're asking for the impossible.
If the signal isn't so good, you need to be able to "capture" as much of it as possible. An omni directional antenna is designed to pick-up signals from any direction but the trade off is that it perfoms relatively poorly. A directional antenna has the opposite characteristics - ie it performs well if the signal comes from one particular direction but very very poorly if it comes from anywhere else.