UKH

What’s the best beginner crag near York? Daughter wants to take her boyfriend from York climbing, she’s done little and he’s done none. I can lend them necessary gear and bouldering mats.

Brimham might be worth a look? 

Scugdale? Short, loads of diffs and v diffs, good views not too many people.

I'll second that. Scugdale is far and away the best 'beginner' crag in the region, loads of easy routes, slabs cracks and juggy prows, easy communication, easy belays, plentiful simple gear placements for early leads. Lovely location too.

With careful route selection and some wandering about Brimham can be made to fit the bill but you really need to know your way around which it sounds like they don't.

Beyond that I'd head for the honeypots of the eastern edges, they're popular for good reason. The far end of Stanage is just about the closest by car but I suspect for beginners Bamford or popular end is worth the extra drive.

jk

How little is "little"? When I was a beginner to climbing, I tried Almscliff and Brimham, which put me off gritstone for a couple of years. But though a beginner to climbing I had a few years of hill walking and scrambling behind me, so my two go-to crags quickly became Peak Scar and Whitestone Cliffe. But these are very much mountain style crags (including their fair share of suspect rock), and very much not recommended for any beginner without that sort of experience.

Otherwise - another vote for Scugdale. Park Nab is another with some good well-protected low grade routes. Also since you mention bouldering, perhaps Slipstones, the right hand end specially has some lowball problems with flattish landings - but I'm not a bloderer so this may be a poor recommendation!.

Good point about Brimham, finding the gems can be tricky. Scugdale is a good shout. For some variety there are plenty of easy routes at the Wainstones, I cant remember how setting up belays was though. It does have a longer walk in, which makes for a nice day out. 
For a more local option, wetherby is nice for a quick session 30 second walk in, loads of easy (font4-6) bouldering. One negative in the current state of affairs is that the crag is right next to a footpath so social distancing may be difficult if people walking past aren't bothered about it. It also might be better after a few dry days. Definitely not the best crag in the world, but good for a quick local trip.