Elvington or Breighton (Or both, they're only about 10min apart) are safe options as there's the museum at Elvington and lots of Pontious Pilot-era kit at Breigton (If that's your bent). Elvington is difficult to miss (2.5mi of runway - miss that and you probably shouldn't be flying), Breighton can be a bit of a pain to spot. Landing fees sensible at both, Breighton has a better cafe. Watch out for gliders from Pocklington and Rufforth, and Elvington is on the ILS for Church Fenton - likewise the area's pretty busy with Tucanos from Linton during the week.
Neverthorpe is as short as it is wide (Shortest licensed strip in the UK, apparently) so check your performance before you go there...