Try Kirknewton by Edinburgh, loads of black cabs to suit your needs and only 15/20 mins into city centre Approx £12/£15 each way.
Landing fees at Kirknewton,donations accepted.
Here are a few handy numbers.
Kirknewton 01506885555
Edinburgh ATC(for booking,Kirk is in the zone) 01313336239
Edinburgh atis 01313336216
City Cabs 01312281211
Central Taxis 01312292468
Plenty to do in Centre,nice big park for the kids and loads of kiddy friendly restaraunts and an amazing zoo.
Check out Mobility Scotland if your requirements include a wheelchair as I have seen them in the city centre with free chairs(also battery powered) during the summer months.