Hi Carol,Burnham on sea is ok, but futher round the coast ... west, is better!! get past minehead, and the scenery gets stunning, i love the north somerset/Devon coastline!!
Minehead to Illfracombe is lovely, you'll pass Dunster castle ...well worth a visit!, Lynton Lynmouth, Porlock, it really is nice! the road touches on the north of Exmoor too so you have views both ways!
From Burnham your not far from Cheddar gorge, great place to visit too!!
Thats if your definately staying at burnham ...but like the others have said, theres loads of beautiful places to visit!! the lakes, North Yorkshire, Peak district, Cotswolds ...i could go on and on.