We live in Suffolk too,just outside Woodbridge and there is lots to do,
I agree with Sutton Hoo and Walberswick is great for the beach.Framlingham Castle is always nice and the market square is worth a bimble around.
There are some great walks around Woodbridge and there is also the Tide Mill etc on the River.If you walk up the River (tarmac path so fine for buggy)there is a good playground at Kingston Field)
Easton Farm park is one of my children's favourites,animals to feed,tractor rides etc.Just up the coast from Southwold is Kessingland Zoo,I'm not very keen myself but it is apparently a good day out.
A bit further afield is Bressingham near Diss with Steam trains to ride on nad beautiful gardens and a Dads Army exhibition! and we had a super day out there last week.
Also at Dunwich you can walk on the cliffs and see if you can hear the Bells from the lost city beneath the sea.Also very good Pub at Dunwich called the Ship.Snape maltings is also worth a visit,nice shops and again Pub,Plough and Sail,not the Crown as they do not allow children in.adn also a nice tea room in the Maltings.There is also an RSPB place near there which is beautiful and you canwalk to the beach.
Thorpeness mere is lovelly you can row round the mere and then pop down to Aldeburgh for the best fish adn chips in the County,also some nice little shops in Aldebugh although it has become a bit "Hampstead on Sea" for me!You can also do trips on the River on "Lady Florence"and there is a small cinema in Aldeburgh and one in woodbridge at the Riverside.
If your 16 year old is quite confident you can get the train from Southwold to Ipswich I think,not the most exciting town but it has all the usual things.Woodbridge also has a bowling Alley at Martlesham just off A12 and this is next to a soft play place so could kill two birds with one stone.
DO NOT MISS THE NEW PIER AT SOUTHWOLD THERE ARE SOME HYSTERICAL SLOT MACHINES HALF WAY UP THAT DO THINGS LIKE TELL YOUR FORTUNE FROM PUUTING YOUR SHOE IN THE SLOT OR SITTING AN AM ARMCHAIR TO TIME TRAVEL!!GREAT FUN FOR ALL.
iF you have any questions post again and I will try to help,there is lots to do and best of all Suffolk is a beautiful place with fantastic scenery ,
P.S. check out the Summer Theatre in Southwold and Aldeburgh it is run by Jill Freud and has a different production every week plus childrens shows in the day you will be able to pick up a programme in the Tourist Office.