I had a bank holiday weekend there a couple of years ago. You've obviously got the Great Orme mine to visit - it's very impressive! Capel Garmon is a must see too - we went in lambing season and the noise from the herd was incredible...

Additional to the other suggestions I'd say a trot round Anglesey is a must - we did most of the sites there in a (long) day. Lots of dolmens etc to see there.

We also headed over to Harlech way but didn't venture off road much - there are some stone rows up on the hills above the town that might be worth investigating.

The weather (and my health at the time) stopped me getting up to Penmaenmawr.

Enjoy!!