Gorleston is a residential town and nothing like GY, it isn't quaint like Southwold or Wells but has a very large sandy beach, is very safe, has lots of eateries etc and is on the A12 so very easy (by Norfolk standards) to get to other places.
GY seafront is a good day out for holiday makers and had lots of money ploughed into it, it's the residential and shopping areas that have gone down hill (most locals shop at the out of town retail parks so lots of shops in town have closed), the seafront itself with the venetian waterways is nice, the circus is one of a kind and arcades, Pleasure Beach, crazy golf etc children will love it if they've not been somewhere similar so don't discount it completely.
If I was coming on holiday from London I'd stay at Potters, Hopton caravan park or Fritton if I had a large budget, or slightly fourth out Waveny River Centre (20 mins from a beach but is on the Broads)
Use Gorleston beach, you can crab off the promenade if the weather isn't good, although we get very little rain in the summer.
Day trips wherever you stay but include journey times from gorleston:
Pensthorpe nature reserve (60-90 mins, amazing climbing frames indoors and out)
Dinosaur Park (60mins ish)
Bewilderwood, (age 3 - 12, 40min drive), pop into Wroxham barns on your way home
Norwich, (35 min drive, visit the castle & themed afternoon tea at assembly House)
Beach ride from Pakefield riding stables (20 min drive)
Oulton broad to watch the race boats (Thursday evenings) (15 mins)
Oulton broad to hire a motor boat, canoe, kayak or paddle board.
Beccles Lido (30 min drive)
Carlton marshes nature reserve (15 min drive free entry and parking, brilliant climbing frame)
Spend the evenings in GY enjoying the lights, rides and arcades etc, fireworks at 10pm on Saturdays. Go to the circus.
I'd spend one day and drive up to Cromer for rock pooling and crabbing and a dip in the sea, on the drive back visit the seals at Horsey and the lighthouse (and DD loves the little zip line on the cliff) at Happisburgh.