Interesting....I've never come across a marina that would not let me have a propane grill ON my boat. On the dock...no, they don't allow that, but on my boat; well, it's my boat. How is that different from a sailboat that runs its galley on propane? I've never seen a marina that banned boats with gas stoves inside.
Anyway....I have a Weber gas grill on the flybridge with a tank that is up there, outside. I want to get a fiberglass tank at some point as the regular one leaves the rust ring that I have to keep cleaning. We put our grill on the flybridge because we have an unusual amount of space up there, and we could not find any railing attachments for the Magma grills since our railing is extra big - it was modified with the boat was an inspected vessel. I do not like having to pass platters of grilled food up and down the flybridge ladder which is why I really wanted it attached to a bow railing. Oh well...it's what we have for now.
Our grill is not the greatest, but it gets us by until we can build in the grill we really want. We don't think it gets hot enough for our cooking preferences. It does OK, and we can sear meats, but I think it could be better.
I don't think I have enough juice capacity to run an electric grill. I had one of the JennAir electric grills just about my whole life when I lived on land. I do like them, but I could never quite get the flavor that a flame under the meat gives. I mostly used it for cold winter days or just plain cruddy days when no one wanted to tend the big grill outside.