I've cycled the bits between Sherriff Hutton and Leeds quite a few times, the route is a bit fiddly but perfectly pleasant. Between Castle Howard and S.H. is Bulmer Bank which is a challenging 1 in 6 down and then straight back up again! Alternatively you can go via Terrington and then turn left down Terrington Bank.
When you get to S.H., turn left at the mini roundabout (NB It's straight on if you've come from Terrington Bank) and go down the hill through the village, all the way out until you get to the Cricket Club on the right, which is over a mile out of the village.
Turn right. In a couple of miles on the left you pass a farm right next to the road that always makes me think of the US prairies, big farm buildings and no field boundaries in sight! Just after it is a small lane on the left alonside a wood. Go down that (it's only short) and then turn left at the end. In another couple of miles at the T junction turn right into Sutton on the Forest, past the swampy woods on your right.
In Sutton turn left at the mini-roundabout and go through the village, just keep on going past Sarah Cameron's folks mansion (Sutton Park) avoiding any temptation to go any further over to the right!
Keep on going into Huby, round the sharp right hand bend and then turn left towards Tollerton. Past Burn Hall and up to the A19 which you cross over and into Tollerton (bit of a dodgy junction TAKE CARE).
In Tollerton turn right towards Alne.
This next bit is my commuting route, after much trial and error, and goes the prettiest way with the least traffic:
In one mile, at Alne cross, go left towards Aldwark, keep going over the rickety toll bridge (3 or 4 miles)
At the T junction (another mile or so after the bridge) go left towards Little Ouseburn over the humpback bridge and past the church. Don't go into L.O. though, go straight on to Thorpe Underwood, past the private school.
After a couple of miles you cross over the fast B road that you would have had to cycle along if you had gone through L.O., pass the cricket ground and turn left towards Whixley.
Take the next turn right in about 200 yards (Franks Lane) and go into Whixley Village. Go down a short hill past the village hall on your left and then turn right. (There are two right turns and they both end up at the same place so it doesn't matter if you get the wrong one).
Follow the road round and up the hill until you get to the A59. Cross over on to the single track road opposite. About half a mile down is a manned level crossing that will be closed, but with a bike you can cross through the kissing gate beside it. A couple of miles further on and you get to a T junction with the A167. Turn left and in about half a mile go right at the roundabout over the motorway, follow that road to the Bridge Inn (you're now back on the same route as if you had gone via Cattal) - you should be able to pick up the cycle path there (on the right hand side of the road) that used to be the northbound carriageway of the old A1 and is fine for road bikes. Keep going all the way down there until you get to the roundabout near Wetherby. Turn right into Wetherby.
In about a mile pass the Esso garage on your left and the Total garage on your right, then at the mini roundabout go right (St James Street) until you get to the A661 Spofforth Road. Go right then shortly left onto Linton Road, which runs roughly parallel to the A58, through Linton and all the way into Collingham.
At the end of that road, by the school, you get to the A659, turn right and cycle up the hill (it's nice and wide, so OK) towards Harewood.
Once you have been out in the country again for about a mile turn left towards Wyke and East Keswick. This takes you along Wyke Ridge and eventually down to the Leeds Ring Road, cross over and straight on takes you up towards Roundhay Park - and I assume you can find your own way to Meanwood from there!
Have fun!
