It depends what you want when you visit! For curmbling old architecture, graffiti and chav spotting, you can't do better than Rhyl!
Only joking, but the most obvious attractions for me in North Wales are the steam railways. The narrow gauge ones are pretty well know, most are reachable from the main line, Welshpool, Tywyn and Porthmadog should not be missed if you want narrow gauge.
The stnadard gauge line at Llangollen is a short bus ride away from either Ruabon or Wrexham. Llanberis and Bala for the lake railways can also be reached by bus. The Snowdon Mountain Railway is a bit expensive and reliant on the weather, you could easily see nothing at all at the summit, as happened to us in 2009!
Other than that, there are lots of castles, old mines, Lloyd George's house near Criccieth, Llandudno - the choice is vast!