In reply to Lrunner:
Tim Davies has the best suggestion when considering your requirements:
Weather is generally better - or at least less wet - a bit further along the coast from Anglesey/Bangor area. Not that surprising as the prevailing weather is from the west but it's surprising how just those few miles can make a difference.
Close to the A55: is this because you will be using it daily or often for work etc? If so, it's definitely better to be close-ish to it if you need frequent access. The A55 is the main (pretty much only) W-E thoroughfare so everybody uses it for commuting and, as a result can get busy and slow, with even more traffic coming into Wales on a Friday evening and going out on a Sunday or Bank Holidays etc. Roadworks or an accident can quickly bring it to a halt, not much you can do about this, though. There are exceptions: going onto Anglesey in the morning is normally quiet as all the traffic is travelling east and vice versa in the evening.
Close to hills: for running there are ideal hills behind Conwy (Northern Carneddau really) and areas such as the Clwydians a bit further east. Don't know about running clubs.
Close to a wall: The Beacon in Caernarfon is the biggest wall around here, Indy wall at LlanfairPG is about the only other. I'm not fully up-to-date with local walls so there may be some other one tucked away but otherwise I think you're looking a trip east over the border for most others. Unless you lived right next to a wall you'll probably just have to accept a bit of a drive to one; I'm assuming your other criteria take precedence over proximity to a wall. Also worth bearing in mind that, assuming you'll be using the wall mainly in winter, you'll probably have next to no traffic, whereas someone in say Manchester may take a lot longer to get to their wall even though it's closer to them.
On a similar theme to my last point, just accept that you'll have to drive to crags as well: even if you lived in somewhere such as Nant Peris, you'd still have to be up and away early to drive to and get a parking place at the popular crags - ok, you could walk up The Pass but you'd still have to drive to somewhere such as Ogwen or Tremadog and be battling all the other punters. I guess my point is, put your other daily considerations over having a couple of crags on your doorstep. You'll still be able to get out easily on the light evenings, obviously.
The further east from Bangor, the less Welsh is generally spoken, certainly as a first language. It's quite a sharp cut-off: it's heard all round Llanberis, Caernarfon, Anglesey, Bethesda etc but go just down the A55 to Llanfairfechan, Penmaenmawr etc and it's a lot less common; Conwy and Llandudno are similar. I believe all Welsh state schools teach Welsh and English, each to a greater or lesser extent. I am not sure of the ins and outs of this, I'm sure someone else can advise you.
Some specific places to consider:
Conwy: good location, nice town, very touristy, good access to hills. Probably not cheap due to tourist/picture postcard tax.
Llandudno: good location, good weather, good facilities, regularly invaded by coachloads of (old) tourists.
Llandudno Junction: don't know loads about it, a bit more 'functional' than the previous two places, I think. Very handy for A55 and trains, Conwy is walkable. Could be worth looking into.
Maybe look at places a bit inland such as Denbigh, Ruthin etc. You are moving away from the climbing wall requirement at least, though.
Hope this bit helps, happy to try and answer any more specific questions or feel free to PM me if you prefer.
Post edited at 21:37