Having grown up in Ripon here is some climber-based info:
Brimham (inc Eavestone, Whitehouses etc.) - 10 minutes away
Harrogate Climbing Centre (nearest wall) - 25 minutes with no traffic, 40 minutes in bad traffic (the traffic is often bad once you hit Harrogate and the wall is effectively on the other side of town from where the Ripon road arrives).
Slipstones - 30 minutes
Almscliff - 40 minutes
Kilnsey - 50 minutes
Closest NYMoors crags e.g Wainstones, Highcliffe Nab, Scugdale - about 50 mins
Leeds Walls - a good hour
Moorland grit - 1 hour
Malham - 1 hour 10
In climbing terms Ripon is a really good place to live if you like Gritstone bouldering (and trad to a lesser extent) given that Brimham is very close and Slipstones and Almscliff are close too. For sport, Kilnsey is pretty close, as are some other crags e.g Trollers Gill, but Malham still feels like a bit of a trek (although 1 hour 10 isn't bad for Malham and you don't have to drive through Bradford...).
As a place to live Ripon is really nice. It is a market town with a square in the centre and sufficient shops, pubs etc. Good bus services. No train station. The town itself is really nice to walk around and it's right in the middle of some great countryside for cycling and walking. There are some good schools, particularly Ripon Grammar School, if that floats your boat. It's a pretty quiet place that doesn't really change - especially in its tendency to vote Tory. You're close to Leeds (50 mins) York (45 mins) Harrogate (20 mins) and, in your case, Northallerton (15 mins) making it a good location for jobs etc. Lots of nice villages and minor crags to explore nearby.
Let me know if you want to know anything else.