Cornwall and Devon are popular for good reason, best avoid peak season for crowds and traffic. So June and Sep. I like Salcombe out of sesson also Dartmouth.
Poole is great for a long weekend, get the kids signed up for some water based activities. Sandbanks and the dunes over the chain ferry at Studland, Swanage, a pint at Square and Compass, bit of walking, bit of beach etc
New Forest with a day trip to Yarmouth (boats amd small beach, fish and chips in Saltys) from Lymington. Maybe even a long weekend on the IoW
As above do a long weekend in Normandy/Brittany. Ryan Air (horrible but they fly to places others don’t) go to Deauville (great beaches, food etc) and Dinard (for St Malo) for example. Squeezy Jet may do also. Check destinations from Southampton too, great little airport