There are a couple of cycle tracks that I usually use, though how you get to them depends on where you are coming from and they aren't entirely on-road, though if your bike is indeed a hybrid, there is no reason you should have any problems.
The more common route leads to Hornsea, usually I join onto this down Kestral Ave and using Google Maps it shouldn't be too hard to find your own way onto it -
Here.
There is a nother route that leads to Withernsea, it has one small problem in that some idiot farmer in Otteringham has fenced it off, he has no valid argument however so everyone just rides accross his field to get to the next segment of track, this one is a little longer and harder than the Hornsea track, and the terrain can be a little rough in places, but as long as you are careful it shouldn't be a problem - hey, if I can run a 90 year old Raleigh Tourist on there without problems then a modern hybrid should have no problems. I usually join this track from Marfleet Lane, via the road either side of the bridge.
Here.
Of course, with either track, you could probably just follow the roads instead, but it would take longer. I'm think that once you reach Hornsea there was another route that lead to Bridlington and even further though I don't remember where and am unsure of this. Another route I know of is the Trans Pennine Trail, but there is some off-roading involved with that and it is at least 70 miles long, which is something that could be acheived one-way in a single day, but getting back isn't something you would be doing on that same day, it ends up around Filey somewhere as far as I remember.
Hopefully those should suffice as they are pretty much all I know of, other than riding over the Humber bridge, and there is naff-all worth seeing over there in my opinion, except those Lincoln scummers.
