I live on Holy Island. Here, and Anglesey as a whole, is a real pull for sea kayakers – challenging, interesting and as it’s an Island you can always find good paddling in any wind direction, and state of tide, somewhere.
I know these waters well, but more as a sailor than a paddler, but I would be a little concerned about going out in a kayak in February. But if you choose to do so, Treaddur Bay / Porth Dafarch would be doable in a gentle onshore wind (W / SW) although there will still be some swell. Alternatively, Holyhead Harbour and paddle up and down the prom in a N / NW wind.
The Holyhead Country Park is interesting both from nature and maritime industrial perspectives and there are some trails which run along Rocky Coast to it on which you could cycle.
For other things to do: South Stack and the Range is amazing, the Sea Zoo in the SW of the island and Melin Llynon for the doughnuts!
Hope you have a great time!