I've been to st Bees loads of times hun but not on holiday really just coz I grew up in Cumbria not too far from there. I can't comment on the beach really as I've only been to the very far top part rock climbing and camping.
The village itself is nice and small but not much there really. But if you like walking etc and want to explore the lake district then it's a nice base as you have the lakes directly to the east and the beach to the west so a bit of both. It's also idealy placed to visit the western lake district which is less popular than the busy parts like windermere/bowness/ambleside etc but IMO far more beautiful and less spoiled.
It's right next to Whitehaven so if you need bigger shops (nappies etc) you're not too cut off. I don't really have much advice on places to visit, it's also right next to Sellafield
(nuclear power station) but I think the visitor centre would be a bit old for Harrison yet. I suppose it depends what you want from your holiday I guess, I'm a bit biased because I love the lake district - it's my home and I miss it every day. Hopefully there will be someone who can advise from a holiday point of view
xx
