Most direct route to reach Rimini is from Florence, though it's still a bit of a hike: about 3 hrs by train, with a change in Bologna (you can also take a more scenic slow train through the mountains, but longer still). Either way, probably should schedule a least a night in Rimini if you really want to go. Weather in May should be nice, mild and not too hot. Might be a little cooler up north in Venice, but not by much.