Yorkshire climbs within sweating distance of York

Glad you enjoyed it.

I must admit that when I read your post about representing your country, I worried that  the Wolds may have been a little sedate. Perhaps moors and high dales next visit eh?

Try out strava heat map. For popular routes

Loads of great advice already but given you have a car, I'd be inclined to drive to Helmsley or Kirkbymoorside and start there as you right on the edge of the moors. I'd say Rosedale chimney is a must if you want to really test yourself. When it gets that steep that you feel you are just holding your hands above your head, you'll know why people talk about it !
Personal favourites of mine are Bransdale (fabulous scenery and very little traffic) and the hills around Hawnby, Rievaulx and Old Byland (same reason).
I don't know what gearing set up you have but there are loads of >20% gradients where you'll be grateful for a bigger cog on the rear wheel !
As for the ale, Theakstons and Timothy Taylor are my favourites but if you are around Helmsley, they have their own micro brewery and it's a fine drop.
My only other advice would be to avoid the A170 (a fast, busy tourist road replete with crap drivers) and be careful on the B1257 as that one attracts the top gear petrolhead crowd.

Theakstons are great beers.  Watch the Old Peculier though, it's strong and will take your legs from you if you are walking, never mind cycling.  I used to like XB, great flavour and mid strength...mmm...

Not sure if White Horse Bank is the same as Sutton Bank?  Sutton Bank climbs the North Yorks Moors from Thirsk, but it is likely to be very busy.  I wouldn't fancy being half way up it with some idiot in a caravan or truck trying to get past.  Once you're up there though, lots of quiet and quite remote roads.  

Wold top is pleasant enough but is no great shakes IMHO.
Haven't visited Malton for some years but the 'New Malton' pub gets decent reviews and should have a good selection of beers

Remarkable cheap soccer jerseys

Do you have a GPS device?  If yes is it a Garmin?

Re the North York Moors - I went up Murton Bank, White Horse Bank and Boltby Bank at the weekend.  Excellent climbs.  However, I couldn't spit quite that far from Stamford Bridge and there are potentially a fair few miles between the three if you were to climb them in that order.  Book your next holiday home in Osmotherley, Egton Bridge or Grosmont in the North York Moors and have a great time. 

If you can tell us how many hours you can spare and how many miles you would like to cover there are plenty of cheeky climbs around the northwest escparpment of the Yorkshire Wolds.  I would be happy to put together a crisscrossing route that passes through Thixendale a few times and takes in most of the climbs out of there.  I may be a tad biased, but I reckon it is a superb area in which to cycle.  (The best bits on ITV4's Tour de Yorkshire trailer were filmed around Thixendale - and Millington mentioned upthread.)

In Simon Warren's "Cycling Climbs of Yorkshire: A Road Cyclist's Guide" seven of the 75 hills are in the Yorkshire Wolds.  Two you can discount straight away because they come off a busy A road and one or two more are a bit too far south to be included in a likely route.  But the remaining three can easily be supplemented by several testing climbs close together that linked up would make a rewarding route.  Stamford Bridge is an ideal place from which to explore the Wolds.  The roads are is eerily quiet. 

Some further reading on climbs in the area:

http://eastyorkshirectc.org.uk/hill-climbs-on-the-yorkshire-wolds

And if you happen to like Strava art routes shaped like a rabbit changing the belt on an upright vacuum cleaner this one gives an example of some of the lumpy bits around Thixendale:

https://www.strava.com/activities/576006201

Cheers. 

A little warmer upper without having to drive anywhere with a couple of 12% and a wicked 20% descent out of Wharram just before hitting a twisty bit :D. nowhere notable but lots of quiet back roads.

Approx 53 miles & 2800ft

Stamford - Pocklington - Bainton - Wetwang - Wharram le street - Malton - Coneysthorpe - Barton hill - Harton - Bossau - Buttercrambe - Stamford

As above, plenty of short steep stuff if you look around and get into the Dales and out of the Wolds.

There are no end of awesome climbs within spitting distance of York, the only limit is your time and fitness. You don't need to actually get to the moors to experience great riding though. Personally I'd push north up through the villages and wolds heading to Nunnington and then north towards Kirkbymoorside. I'd head up past Fadmoor/ Gillamoor and north to Blakey bank. It's one of the toughest in the moors and a real leg burner. Depeding on time and fitness you can turn right at the top and begin your return, or left, then right and descend the other side of the valley to Rosedale. A right in Rosedale turn will let you ride one of the steepest roads in the UK, the legendary Chimney bank a true 33% killer. A great descent follows to hutton le hole and then you can wind you way back home via Castle Howard.

If feeling really fit there are longer routes if you drop down from the top of Blakey bank into Castleton and select one of the many routes back over the moors from Danby or Egton Bridge. Any route back over will demand another 25% er and if planned could still get you into Rosedale and get the Chimney ticked off. These roads are seriously grippy and if you don't do much riding shouldn't be underestimated.

Alternatively as the previous poster suggests you could just surf the N Yorks escarpment and take in any number of classics, Boltby bank, Sutton bank (best avoided), White horse bank and Wass bank. A decent ride would be to ride to Ampleforth up Wass bank descend off the top down to Rievalx Abbey via Scorton,head to Helmsley, Harome, Castle Howard and ba through the flatlands. Wherever you choose you won't be dissapointed. Enjoy!

Not in the same league as the NY moors as far as climbing goes, but for quiet, undulating roads with the odd short but steep pull, head south east on the 'Way of the Roses' to Millington Dale and Nunburnholme. East to Bugthorpe and Thixendale. North east to Acklam and Leavening. Plenty of OS chevrons available and all possible in a day's ride.

Straight out the front door and the Wolds're your oyster.

Which side of York are you on ? The Vale of York is very flat so you'll need to head up to the North York Moors to find hills.

You could take in White Horse Bank and Boltby Bank within a 70 miler from the city. If you can avoid the A170 there is lots of nice hilly riding up to Helmsley and Rievaulx.