In reply to owensum:
Firstly, I'd try to choose your climbing days carefully if you can - when there's a cool breeze blowing, climbing on the grit is wonderful, but on a still humid day with the midges out, it is hell on earth.
For routes, I'd revisit Alsmcliff, which has a handful of classic routes, this video is a good guide to the best of them:
http://www.ukclimbing.com/videos/play.php?i=1134
In Yorkshire generally the bouldering is far better than the routes. I think Bridestones is an amazing venue, with superb problems taking real lines (much of the bouldering at Almscliff, in contrast, is of the arse-scraping arbitrary eliminate variety). Another wonderful bouldering crag is Slipstones which is very easy to get to from York - you'd be best finding a partner with a couple of pads on here. People might go on about Caley, and while it is one of the best bouldering crags in the UK when in condition, it is right by a main road, covered in litter and graffiti and only really a nice place to climb in spring and autumn.
If you're wanting to do more routes, I would spend more time in the Peak if possible, where the routes are about a thousand times better and more plentiful. At Stanage, make sure you have a pad or two for the classic highball boulder problems at the Plantation: Crescent Arete and Not To Be Taken Away are arguably better than any of the routes on the crag. Cratcliffe is a must-visit crag, so is Hen Cloud - the routes at these two are big (for grit) satisfying pitches.
In summary, I reckon the best of grit is:
Slipstones and Bridestones for bouldering;
Almscliff, Cratcliffe and Hen Cloud for routes;
Stanage for famous names and convenience.
And if it's hot, humid and still (or of course raining) don't expect to have fun at all.