I used to live in North Devon. Bideford to be honest isn't much of a town, however you are well placed to go to lots of pretty areas.
Milky Way is a small theme park which is really good, plus the Big Sheep is a good laugh. Both of those are about a 10 minute drive.
You are not a million miles away from Bude, which is a nice beach. Avoid Westward Ho like the plague. You are not too far from Woolacombe, Saunton (which is the other end of the beach from Westward Ho and a thousand times nicer) and Croyde which are the best beaches in Devon - it shoukd take about 45mins to get to those.
There is another cracking theme park in Kilkhampton (about 15 mins from Bideford) but I can't remember for the life of me what it's called. Oh, when I say theme park I mean Devon theme parks so they are small, family run and actually really nice for little kids.
Barnstaple is the best town for shopping, but that's not saying much. But there is a cinema, ten pin bowling, soft play etc for when if it rains.
Oh and also Combe Martin Wildlife Park and Exmoor Zoolofical gardens are excellent - a bit of a trek from Bideford but very nice.
And if you like riding bikes there is the Tarka Trail cycle way, it's flat and you can hire bikes with kids seats/trailers from Bideford town centre - google Bideford Cycle Hire. It's a lovely bike ride (and I say that as someone who hates riding bikes in general).