Best seaside resort near Fakenham is Cromer: paddle-board hire and that sort of thing available. A bit nearer to Fakenham, Sheringham has shops, pubs, cafes, beach etc but prom is a bit ugly and you have to get over the stones to get to the sandy bits of the beach. However, the North Norfolk Coast path on the cliffs between Sheringham and Weybourne is beautiful.
Best beach is probably Wells: it gets busy but is close to (busy, expensive) car park, toilets and cafe. For vast, nearly empty beaches a fair trek from facilities, Holkham, Cley and Burnham Overy Staithe.
No shortage of pubs. I like the Hunny Bell in Hunworth and the Three Horseshoes in Briston, but there’s lots along the coast as well which I haven’t got around to trying yet.
The seal trips to Blakeney Point are great! There are about 4 different companies running them, all from Morston Quay near Blakeney. They do get booked up in the school holidays, so you’ll need to book ahead.
I don’t know about riding but I have seen horses on the beach at Cromer and Holkham, so might be worth an internet search.