I don’t (think) I know @NotMaryP0ppins, but I obviously live very close to her. I’m in the rural HD8 postcode. We’re 10 mins from the M1 at either J38 or J39. We came here temporarily 20 years ago, and we’re still here.
I commute to Leeds on the M1. Takes around 40-50 mins at 8am/5pm, quicker out of rush hour, but I do work on the south side of Leeds, one of the first buildings as you come off the M621. In fact about 10 mins walk from Leeds station! I rarely go by train (Denby Dale is my local station, as the service is only once an hour from my end. There is a bus to Wakey/Train from Wakey option too, which I used to do, but my job requires far too many impromptu site visits for that to be particularly useful to me, and I now get a company car, so I cBt really comment on the reliability of the pubic transport options. There are some Park n rides that my colleagues use.
I love the rural setting + proximity to cities here - Leeds and Sheffield are within easy reach, and Manchester and Liverpool to a lesser extent. Great for airports, not so much for commuting. Huddersfield, Wakey and Barnsley are 20 mins away. Holmfirth and Penistone market towns, both with a lot going on, are closer. Excellent theatres, museums etc in all those cities.
My dc (8 and 11) are in the 3 tier first/middle/high school system her and doing well in the high performing schools. Extra curricularly there is a huge choice of football, cricket, rugby, tennis, bands, choirs, scouts/Cubs/beavers and about 101 other things they don’t do going on.
We often go out to the Peak District and Dales. I’d really say the only things lacking are
1- the coast is a bit far, 1.5-2 hrs
2 - public transport to Leeds could be much better
Your budget would get you a lovely house comfortably.