We used to stay there every year. Further along the Llyn Peninsular, near Tudweiliog and Penllech.
Our family still refers to "Porthmadog Weather" which is when the rain is beating down continuously all day.
There's beaches. Slightly depends on what you want. My memory is the choice between a beach with toilet facilities, café and paying for a car park-and crowded in nice weather.
Or a 2 mile walk along the cliffs from a free car park with no toilet, café and lots of seaweed. That, unsurprisingly, is less crowded. Unfortunately my parents preferred that. Even in the rain. We were one of the first families to take one of those big tent-like structures down to the beach. That was so we could remain there through "Porthmadog Weather".
If you like long walks and castles there's lots. Some of the castles might be quite fun for the little one. They're not when you're looking round one (in Porthmadog Weather 
) for the fourth time.
Don't climb up Snowdon promising you will go down on the railway. You may find your dd hasn't forgiven you in 30 years when you find it isn't running. 
There are some adventure places and you can also do things like boat trips round Anglesey, and the steam railway. I can't comment on those. They were too expensive. Well, too expensive for my parents who I will also note would do the 20 mile detour to avoid the 5p toll. My df tried to dress it up as the "scenic route". We all knew his real reason.
Dbro got car sick on windy roads. That was interesting if we were doing anything other than going down the drive, so the 20 mile detour turned into 10 x 2 miles with a break every 2 miles for him to leap out of the car.
Once he lept out of the car while it was moving because a bee flew in a window. Roads in Wales are just as hard when you land on them as English roads. He also didn't like blood. That's not a good combination.
My dp thought a fun day out was to sheepdog trials. Watching dogs being chased by 6 sheep round a field was quite entertaining for the first 2 or 3. The latter 30 dogs were not quite as fun. Refer back to Portmadog Weather and think about that in a field with no shelter. Actually, perhaps the entertainment was meant to be pushing the car out of the mud at the end of the day. The real attraction for df was that it was free to watch anyway.
We loved it there, and begged to go back year after year.