Leeds to Scarborough. Easiest would be train, takes about 90min, costs about £10 for single fares (so £20 for the return), or ~£27 for a return. Mostly the trains run to time (or very close to it).

Of course Leeds-Bradford Airport is nowhere Leeds... This adds a 1/2hour bus trip to the journey. The 757 runs from the airport to close to the railway station in Leeds. No idea what the bus will cost.

ETA: you're not looking at much change from £60 for the two of you. Car hire is going to be £80+ for the Friday to Sunday/Monday.