Tap On Tap Off allows a ticketless journey on Coastliner 840 from Leeds all the way to Whitby (although you could argue the Tap Off is pointless as you'll still be charged £3 anyway) a journey of roughly 4 hours and some beautiful scenery as you cross the North Yorkshire Moors.
The same applies for the 843 allowing a ticketless journey from Leeds to Scarborough, which takes roughly 3 hours
20 minutes End to end, although it's less scenic than the 840.
Most divisions of First Group now allow tap-on as well. So from Leeds you could get to Huddersfield via a variety of different routes, which looks like it would add on roughly another 2-3 hours based on my skim-reading of timetables.
Huddersfield is an extremity of TfGM's massive tap-on system covering the whole of Greater Manchester, so, after sitting on the 184 into Oldham, you can travel some huge distances. For example, we could circumnavigate a huge chunk of Manchester: Oldham - Ashton (409) - Stockport (330) - Manchester Airport (313) - Altrincham (288) - Trafford Centre (245) - Wigan (132) - Bolton (607).
From Bolton we could proceed via Transdev routes 1 and 152 to Preston, by which point we would have travelled, by my rough measurement, somewhere between 150 and 200 miles since we left Scarborough!
I got bored at this point, but Preston Bus and Blackpool Transport both seem to have tap-on so I'm sure someone can take it from here...