In reply to Stuart Williams:
Hey Stuart.
I live in the area and can confirm there's tons of great off road running nearby. You're within a 15/20 min drive of the Sychnant Pass (3 different car parks in close proximity, all free) which gives you access to Conwy Mtn on one side of the col, and everything on the south side of the col is great terrain (good advice from Steveriley - those races tramp over this area). From there, you can make it across to Tal y Fan and back well within your 15km and there are numerous combos you could do with the trails that tot up to quite a lot of ascent for distance covered. I find a decent route is to do a figure of 8 centred on the Synchnant Pass, around Conwy Mtn tops over the pass and around some features on the south side, which is a good compromise of what you've asked for of distance/ascent/accessibility.
Going as far as Tal y Fan will probably keep you entertained for a while but if you want more ascent for distance then you could do the drive round to the car park between Tal y Fan and Drum (about 40min from Colwyn Bay), which gives you easy access to Drum and the Cardneds proper. Bit far to go for a regular run perhaps but definitely worth the effort every now and again.
Good luck with the move. It's a brilliant place to be located as a runner, and even Conwy Mtn is a gift to have right there. A lot of the trails are quite soft and knee-friendly (aggressive lugs are your friend!). You could also take a look at a Strava heatmap or similar for an idea of where folks go.
Feel free to drop me a line when you move to the area if you want some more tips or fancy getting out.